Name: ________________________ Class: ___________________ Date: __________
Derivatives Practice - Stewart
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Differentiate.



K(x)   2x 3  1  x 4  2x 



Select the correct answer.
a.
6x 2  4x 3  2
b.
14x 6  4x 3  12x 2  2x

 


x 2  x 4  2x    2x 3  1  4x 3  2

 



 3

2  4
3
6x  x  2   4x  2x  1




  3
  3

2  4
6x  x  2x    2x  1  4x  2

 


c.
d.
e.
____
2. Find the equation of the tangent to the curve at the given point.
y
1  4sinx ,  0,1
Select the correct answer.
a.
b.
c.
d.
e.
____
y  4x  4
y  2x  4
y  1  2x
y  4x  1
y  2x  1
3. Compute
y and dy for the given values of x and dx 
y  x 2 , x  1,
x  0.5
Select the correct answer.
a.
b.
c.
d.
e.
y  1.25,
y  0.25,
y  0.25,
y  1.25,
y  1.25,
dy  1
dy  1
dy  0
dy  0
dy  0.25
1
x.
ID: A
Name: ________________________
____
ID: A
4. Find f  in terms of g .
f(x)  x 2 g(x)
Select the correct answer.
a.
b.
c.
d.
e.
____
f (x)  2xg(x)  x 2 g (x)
f (x)  2x  g (x)
f (x)  x 2 g(x)  2x 2 g (x)
f (x)  2xg (x)
f (x)  2xf (x)  2xg (x)
5. The height (in meters) of a projectile shot vertically upward from a point 1.5 m above ground level with an
initial velocity of 25.48 m/s is h  1.5  25.48t  4.9t 2 after t seconds.
a) When does the projectile reach its maximum height?
b) What is the maximum height?
Select the correct answer.
a.
a) 2.8 s
b.
b) 34.428 m
a) 2.6 s
c.
b) 34.624 m
a) 2 s
d.
b) 32.86 m
a) 2.4 s
e.
b) 34.428 m
a) 2.3 s
b) 34.183 m
____
6. The mass of the part of a metal rod that lies between its left end and a point x meters to the right is S  4x 2 .
Find the linear density when x is 1 m.
Select the correct answer.
a.
b.
c.
d.
e.
4
16
8
12
18
2
Name: ________________________
____
ID: A
7. If f is the focal length of a convex lens and an object is placed at a distance v from the lens, then its
1 1 1
  .
image will be at a distance u from the lens, where f, v, and u are related by the lens equation
f
v u
Find the rate of change of v with respect to u.
Select the correct answer.
a.
f
dv

du
 u  f  2


b.
f2
dv

du
 u  f

c.
f
dv

du
uf
d.
f2
dv

du  u  f

e.
2f
dv

du  u  f

 2

2
 2

2
____
 2

8. Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
   
y sin2x  x cos 2y,  , 
2 4
Select the correct answer.
a.
b.
c.
d.
e.
x 

4 8
x
y
4
x
y
2
3
y  2x 
4
x 
y 
2 2
y
3
Name: ________________________
____
ID: A
9. Find the limit.
cos cos  
sec 
0
lim
Select the correct answer.
a.
b.
c.
d.
e.
1
sin 1
cos 1
0
2
____ 10. Find the derivative of the following function and calculate it for x = 25 to the nearest tenth.
y(x) 
x
x
x
Select the correct answer.
a.
b.
c.
d.
e.
1.1
0.9
0.1
0.2
0.3
____ 11. Suppose that F(x)  f  g(x)  and g(14)  2, g (14)  5, f (14)  15, and f (2)  12.
Find F (14).
Select the correct answer.
a.
b.
c.
d.
e.
60
140
24
17
20
4
Name: ________________________
ID: A
____ 12. Gravel is being dumped from a conveyor belt at a rate of 35 ft 3 /min and its coarseness is such that it
forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the
height of the pile increasing when the pile is 15 ft high? Round the result to the nearest hundredth.
Select the correct answer.
a.
b.
c.
d.
e.
0.27 ft/min
1.24 ft/min
0.14 ft/min
0.2 ft/min
0.6 ft/min
____ 13. If f(t) 
4t  1 find f (2).
Select the correct answer.
a.

b.
3
c.

d.
e.
4
27
2
3
2
3
4
27
____ 14. If y  2x 3  6x and
dy
dx
 6, find
when x  5.
dt
dt
Select the correct answer.
a.
b.
c.
d.
e.
948
836
946
928
none of these
5
Name: ________________________
ID: A
____ 15. Use differentials to estimate the amount of paint needed to apply a coat of paint 0.18 cm thick to a
hemispherical dome with diameter 60 m.
Select the correct answer.
a.
b.
c.
d.
e.
2.52
3.24
3.82
2.28
4.11
____ 16. Calculate y .
xy 4  x 2 y  x  3y
Select the correct answer.
y 4  2xy
a.
y 
b.
y 
c.
xy 3  2x  3
y   2 2
x y 4x  1
d.
y  
e.
4xy 3  x 2
1  y 4  2xy
4xy 3  x 2  3
1  y 4  2x 2
4xy 3  x 2  3
none of these
____ 17. The top of a ladder slides down a vertical wall at a rate of 0.15 m/s . At the moment when the bottom of the
ladder is 1.5 m from the wall, it slides away from the wall at a rate of 0.2 m/s. How long is the ladder?
Select the correct answer.
a.
b.
c.
d.
e.
2m
2.5 m
2.3 m
2.8 m
none of these
6
Name: ________________________
ID: A
____ 18. Let C(t) be the total value of US currency (coins and banknotes) in circulation at time. The table gives values
of this function from 1980 to 2000, as of September 30, in billions of dollars. Estimate the value of C (1990)
.
t
1980
1985
1990
1995
2000
C(t)
129.9
187.3
271.9
409.3
568.6
Select the correct answer. Answers are in billions of dollars per year.
a.
b.
c.
d.
e.
16.92
27.48
44.4
22.2
137.4
____ 19. Find the derivative of the function.


y  2cos 1  sin 1 t 


Select the correct answer.
a.
y  
b.
y  
c.
y  
d.
y  
e.
y  
2

2
1   sin1 t  


2
 1  t 2 




2

2
 1  t 2   1   sin1 t   

 

 

 

 
2




 2 
 1  t 2   1   sin1 t   

 

 
2




 1  t 2   1   sin1 t   




7
Name: ________________________
ID: A
____ 20. The height (in meters) of a projectile shot vertically upward from a point 1.5 m above ground level with an
initial velocity of 25.48 m/s is h  1.5  25.48t  4.9t 2 after t seconds.
a) When does the projectile reach its maximum height?
b) What is the maximum height?
Select the correct answer.
a.
a) 2.8 s
b.
b) 34.428 m
a) 2.6 s
c.
b) 34.624 m
a) 2 s
d.
b) 32.86 m
a) 2.4 s
e.
b) 34.428 m
a) 2.3 s
b) 34.183 m
____ 21. Find the derivative of the function.

5
y  3x  1 3  x 4  6 


Select the correct answer.
a.
b.
c.
d.
e.

5
y   20x  9 3x  1 3  x 4  6 


5



4
y   93x  1 2  x 4  6   20x 3 3x  1 3  x 4  6 




5
5




y   93x  1 2  x 4  6   20x 3x  1 3  x 4  6 




5
5




y   93x  1 2  x 4  6   3x  1 3  x 4  6 




5



4
y   x  1 2  x 4  6   20x 3x  1 3  x 3  6 




8
Name: ________________________
ID: A
____ 22. The equation of motion is given for a particle, where s is in meters and t is in seconds. Find the acceleration
after 4.5 seconds.
s  sin 2 t
Select the correct answer.
a.
9 m/s 2
b.
9 m/s 2
c.
0 m/s 2
d.
81 2 m/s 2
e.
81 2 m/s 2
____ 23. Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
   
y sin2x  x cos 2y,  , 
2 4
Select the correct answer.
a.
b.
c.
d.
e.
x 

4 8
x
y
4
x
y
2
3
y  2x 
4
x 
y 
2 2
y
9
Name: ________________________
ID: A
____ 24. Find the derivative of the function.


y  2cos 1  sin 1 t 


Select the correct answer.
a.
y  
b.
y  
c.
y  
d.
y  
e.
y  
2

2
1   sin1 t  


2


 1  t 2 


2

 

 2 
 1  t 2   1   sin1 t   

 

 
2

2
 1  t 2   1   sin1 t   

 

 

 

 
2




 1  t 2   1   sin1 t   




____ 25. The mass of the part of a metal rod that lies between its left end and a point x meters to the right is S  4x 2 .
Find the linear density when x is 1 m.
Select the correct answer.
a.
b.
c.
d.
e.
4
16
8
12
18
____ 26. Use the linear approximation of the function f(x) 
Select the correct answer.
a.
b.
c.
d.
e.
3.02
0.15
7.44
7.4
2.25
10
9  x at a = 0 to approximate the number
9.09 .
Name: ________________________
ID: A
____ 27. Determine the values of x for which the given linear approximation is accurate to within 0.07 at a = 0.
tan x  x
Select the correct answer.
a.
b.
c.
d.
e.
0.71  x  0.48
0.06  x  0.68
1.04  x  1.55
0.57  x  0.57
0.19  x  0.28
____ 28. A turkey is removed from the oven when its temperature reaches 175 F and is placed on a table in a room
where the temperature is 70 F. After 10 minutes the temperature of the turkey is 160 F and after 20
minutes it is 150 F. Use a linear approximation to predict the temperature of the turkey after half an hour.
Select the correct answer.
a.
b.
c.
d.
e.
36
130
134
140
160
____ 29. Two cars start moving from the same point. One travels south at 28 mi/h and the other travels west at 70
mi/h. At what rate is the distance between the cars increasing 5 hours later? Round the result to the nearest
hundredth.
Select the correct answer.
a.
b.
c.
d.
e.
75.42 mi/h
75.49 mi/h
76.4 mi/h
75.39 mi/h
75.38 mi/h
____ 30. The top of a ladder slides down a vertical wall at a rate of 0.15 m/s . At the moment when the bottom of the
ladder is 1.5 m from the wall, it slides away from the wall at a rate of 0.2 m/s. How long is the ladder?
Select the correct answer.
a.
b.
c.
d.
e.
2m
2.5 m
2.3 m
2.8 m
none of these
11
Name: ________________________
ID: A
____ 31. If an equation of the tangent line to the curve y  f(x) at the point where a  2 is y  5x  2, find f(2) and
f (2).
Select the correct answer.
a.
f(2)  8
b.
f (2)  8
f(2)  5
c.
f (2)  5
f(2)  8
d.
f (2)  5
f(2)  5
e.
f (2)  8
f(2)  12
f (2)  5
____ 32. A plane flying horizontally at an altitude of 2 mi and a speed of 490 mi/h passes directly over a radar station.
Find the rate at which the distance from the plane to the station is increasing when it is 10 mi away from the
station.
Select the correct answer.
a.
b.
c.
d.
e.
 495 mi/h
 480 mi/h
 455 mi/h
 970 mi/h
 870 mi/h
____ 33. Two sides of a triangle are 2 m and 3 m in length and the angle between them is increasing at a rate of 0.03
rad/s. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed
length is

3
.
Select the correct answer.
a.
5.045 m 2 /s
b.
0.955m2 /s
c.
0.045 m 2 /s
d.
1.955m2 /s
e.
1.145 m 2 /s
12
Name: ________________________
ID: A
____ 34. If two resistors with resistances R 1 and R 2 are connected in parallel, as in the figure, then the total resistance
1
1
1

R measured in ohms  , is given by 
. If R 1 and R 2 are increasing at ratesof 0.1 /s and 0.4
R R1 R2
/s respectively, how fast is R changing when R 1 75and R 2 100? Round the result to the nearest
thousandth.
Select the correct answer.
a.
b.
c.
d.
e.
0.159 /s
0.145 /s
1.196 /s
0.106 /s
0.168 /s
____ 35. Find the average rate of change of the area of a circle with respect to its radius r as r changes from 5 to 6.
Select the correct answer.
a.
b.
c.
d.
e.
11
6
36
12
8
____ 36. Find the given derivative by finding the first few derivatives and observing the pattern that occurs.
d 30
dx 30
sin x
Select the correct answer.
a.
b.
c.
d.
e.
sinx
sinx
cos x
cos x
none of these
13
Name: ________________________
ID: A
____ 37. A company makes computer chips from square wafers of silicon. It wants to keep the side length of a wafer
very close to 19 mm. The area is A(x). Find A(19).
Select the correct answer.
a.
b.
c.
d.
e.
38
361
48
19
363
____ 38. Gravel is being dumped from a conveyor belt at a rate of 30 ft 3 /min and its coarseness is such that it forms a
pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the
pile increasing when the pile is 12 ft high? Round the result to the nearest hundredth.
Select the correct answer.
a.
b.
c.
d.
e.
0.21 ft/min
1.31 ft/min
0.27 ft/min
0.44 ft/min
0.34 ft/min
____ 39. Find f  in terms of g .

2
f(x)   g(x) 
Select the correct answer.
a.
b.
c.
d.
e.

3
f (x)  2 g (x) 
f (x)  2g x g (x)

 
f (x)  2 gx   xg   g 
f (x)  2g(x)
f (x)  2g (x)
14
Name: ________________________
ID: A

____ 40. If f(0)  4, f (0)  2, g(0)  3 and g (0)  5, find  f  g  0.
Select the correct answer.
11
12
2
3
4
1
a.
b.
c.
d.
e.
f.
____ 41. Let C(t) be the total value of US currency (coins and banknotes) in circulation at time. The table gives values
of this function from 1980 to 2000, as of September 30, in billions of dollars. Estimate the value of C (1990)
.
t
1980
1985
1990
1995
2000
C(t)
129.9
187.3
271.9
409.3
568.6
Select the correct answer. Answers are in billions of dollars per year.
a.
b.
c.
d.
e.
16.92
27.48
44.4
22.2
137.4


____ 42. The mass of part of a wire is x  1  x  kilograms, where x is measured in meters from one end of the


wire. Find the linear density of the wire when x 16m .
Select the correct answer.
a.
b.
c.
d.
e.
6 kg/m
4 kg/m
7 kg/m
1.5 kg/m
none of these
15
Name: ________________________
____ 43. Find the tangent line to the ellipse
ID: A
2
x2 y

 1 at the point
16
4
 2, 


3  .

Select the correct answer.
a.
y
b.
y   6x  3
c.
y
d.
e.
3x  4
3
x 4
3
3
4 3
x
6
3
none of these
y
____ 44. If f is a differentiable function, find an expression for the derivative of y  x 7 f(x).
Select the correct answer.
a.
b.
c.
d.
e.
d
dx
d
dx
d
dx
d
dx
d
dx
 7

 x f(x) 


 7

 x f(x) 


 7

 x f(x) 


 7

 x f(x) 


 7

 x f(x) 


 7x 6 f(x)  x 7 f (x)
 7x 7 f(x)  x 6 f (x)
 7x 6 f(x)  x 7 f (x)
 7x 7 f(x)  x 6 f (x)
 6x 6 f(x)  x 7 f (x)
____ 45. Find the tangent line to the ellipse
2
x2 y

 1 at the point
16
4
Select the correct answer.
a.
y
b.
y   6x  3
c.
y
d.
e.
3x  4
3
x 4
3
3
4 3
x
6
3
none of these
y
16

 2, 


3  .

Name: ________________________
____ 46. If f(t) 
ID: A
4t  1 find f (2).
Select the correct answer.
a.

b.
3
c.

d.
e.
4
27
2
3
2
3
4
27
____ 47. The quantity Q of charge in coulombs C that has passed through a point in a wire up to time t
(measured in seconds), is given by Q(t)  t 3  3t 2  4t  3.Find the current when t 2s .
Select the correct answer.
a.
b.
c.
d.
e.
13
4
2
3
1
____ 48. Use differentials to estimate the amount of paint needed to apply a coat of paint 0.18 cm thick to a
hemispherical dome with diameter 60 m.
Select the correct answer.
a.
b.
c.
d.
e.
2.52
3.24
3.82
2.28
4.11
17
Name: ________________________
ID: A
____ 49. Differentiate the function.
B(y)  cy 6
Select the correct answer.
a.
b.
7c
B (y)  6
y
c
B (y)   7
6y
6c 7
y
6c
c.
B (y)  
d.
B (y)   7
y
7c
B (y)   6
y
e.
____ 50. Find the points on the curve y  2x 3  3x 2  36x  7 where the tangent is horizontal.
Select the correct answer.
a.
b.
c.
d.
e.
 4,71 ,


 3,88 ,


 4,71 ,


 3,88 ,


 3,37 ,


 4,39


 4,39


 2,37


 2,37


 2,37


18
Name: ________________________
ID: A
____ 51. A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is
x(t) 3sin t, where t is in seconds and x in centimeters.
Find the velocity at time t.
Select the correct answer.
a.
b.
c.
d.
e.
v(t)  cos 3t
v(t)  sin 3t
v(t)  3sin 3t
v(t)  3cos t
v(t)  2cos 3t

2


____ 52. Find an equation of the tangent line to the curve 15 x 2  y 2   289 x 2  y 2  at the point  4, 1 .




Select the correct answer.
a.
b.
c.
d.
e.
y  1.11x  17
y  1.11x  3.43
y  1.11x  5.43
y  1.11x  5.43
none of these
____ 53. The mass of the part of a metal rod that lies between its left end and a point x meters to the right is S  3x 2 .
Find the linear density when x is 1 m.
Select the correct answer.
a.
b.
c.
d.
e.
9
3
6
2
1
19
Name: ________________________
____ 54. If f(t) 
ID: A
4t  1 find f (2).
Select the correct answer.
a.

b.
3
c.

d.
e.
4
27
2
3
2
3
4
27
Multiple Response
Identify one or more choices that best complete the statement or answer the question.
____ 55. Find equations of the tangent lines to the curve y 
x8
that are parallel to the line x  y  8.
x8
Select all that apply.
a.
b.
c.
d.
e.
x  y  17
x  y  12
x  y  15
x  y  1
x  y  4
____ 56. If f(x)  4cos x  sin2 x,find f (x) and f (x).
Select all correct answers.
a.
b.
c.
d.
e.
f
f
f
f
f
(x)  4cos x   2cos 2x
(x)  2cos 2x  4cos x 
(x)  4sin2x  sinx 
(x)  4sinx   sin2x
(x)  4cos 2x  2cos x 
Numeric Response
57. If an equation of the tangent line to the curve y  f(x) at the point where a  2 is y  4x  5, find f(2) and
f (2).
__________
20
Name: ________________________
ID: A
58. Find the points on the curve y  2x 3  3x 2  12x  1 where the tangent is horizontal.
__________
59. Find the equation of the tangent to the curve at the given point.
y
1  4sinx ,  0,1
__________
60. Differentiate.
g(x)  x 7 cos x
__________
61. Find f  in terms of g .
f(x)  x 2 g(x)
__________
62. The height (in meters) of a projectile shot vertically upward from a point 2 m above ground level with an
initial velocity of 24.5 m/s is h  2  24.5t  4.9t 2 after t seconds.
a) When does the projectile reach its maximum height?
b) What is the maximum height?
___________
63. Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
   
y sin2x  x cos 2y,  , 
 2 4 
__________
64. Calculate y .
y
x cos
x
__________
21
Name: ________________________
ID: A
65. A spherical balloon is being inflated. Find the rate of increase of the surface area S  4 r 2 with respect to the
radius r when r = 1 ft.
__________
66. Find the derivative of the function.


y  2cos 1  sin 1 t 


_____________
67. Find an equation of the tangent line to the curve.
y
x
at  4, 0.2
x 6 
__________
68. The top of a ladder slides down a vertical wall at a rate of 0.15 m/s . At the moment when the bottom of the
ladder is 3 m from the wall, it slides away from the wall at a rate of 0.2 m/s . How long is the ladder?
__________
69. Find the limit if g(x)  x 5 .
g(x)  g(2)
x 2
x2
lim
__________
70. A company makes computer chips from square wafers of silicon. It wants to keep the side length of a wafer
very close to 16 mm. The area is A(x). Find A(16).
__________
71. Calculate y .
xy 4  x 2 y  x  3y
__________
22
Name: ________________________
ID: A
72. Find the first and the second derivatives of the function.
y
x
3x
__________
73. Find the given derivative by finding the first few derivatives and observing the pattern that occurs.
d 75
dx 75
sin x
__________
74. If y  2x 3  5x and
dy
dx
 3, find
when x  5.
dt
dt
__________
75. The volume of a cube is increasing at a rate of 10cm3 /min. How fast is the surface area increasing when the
length of an edge is 30 cm .
__________
76. If f(t) 
18
3  t2
find f (t).
___________
77. If an equation of the tangent line to the curve y  f(x) at the point where a  2 is y  4x  7, find f(2) and
f (2).
__________
78. Differentiate.



K(x)   2x 3  1  x 4  2x 



__________
23
Name: ________________________
ID: A
79. Find the derivative of the function.


y  3cos 1  sin 1 t 


_____________
80. The position function of a particle is given by
s  t 3  10.5t 2  2t, t  0
When does the particle reach a velocity of 52 m/s?
__________
81. Find f  in terms of g .

2
f(x)   g(x) 
__________
82. Use the table to estimate the value of h (10.5) , where h(x) f (g(x)) .
x
10
10.1
10.2
10.3
10.4
10.5
10.6
f(x)
4.5
3.5
5.6
4.3
2.5
9.9
7.8
g(x)
6.5
5.9
4.7
4.2
5.4
10.1
6.3
__________
83. A spherical balloon is being inflated. Find the rate of increase of the surface area S  4 r 2 with respect to the
radius r when r = 1 ft.
__________

d  h(x)  



84. If h(2)  7 and h (2)  2, find
dx  x  


x2
__________
24
Name: ________________________
ID: A
85. Differentiate.
y
sinx
7  cos x
__________
86. Differentiate.
y
tan x  2
sec x
__________
 

87. Find an equation of the tangent line to the curve y 3 tan x at the point  , 3 .
 4 
__________
88. Find the derivative of the following function and calculate it for x = 36 to the nearest tenth.
y(x) 
x
x
x
__________
89. Find the differential of the function.
y  x 4  5x
__________
90. Find all points at which the tangent line is horizontal on the graph of the function.
y(x)  6sin x  sin2 x
__________
91. Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
   
x sin2y  y cos 2x,  , 
 2 4 
__________
25
Name: ________________________
92. If f(t) 
ID: A
4t  1 ,find f (2).
___________
93. Find the equation of the tangent to the curve at the given point.
y
1  4sinx ,  0,1
__________
94. Find y ,if y 
2x  1.
__________
95. Find the given derivative by finding the first few derivatives and observing the pattern that occurs.
d 99
dx 99
sin x
__________
96. The top of a ladder slides down a vertical wall at a rate of 0.075 m/s . At the moment when the bottom of the
ladder is 3 m from the wall, it slides away from the wall at a rate of 0.1 m/s. How long is the ladder?
__________
97. The height (in meters) of a projectile shot vertically upward from a point 1.5 m above ground level with an
initial velocity of 25.48 m/s is h  1.5  25.48t  4.9t 2 after t seconds.
a) When does the projectile reach its maximum height?
b) What is the maximum height?
___________
98. Find y by implicit differentiation.
8cos x siny  7
__________
26
Name: ________________________
ID: A
99. Find the derivative of the function.


y  cos 1  sin1 t 


_____________
100. If an equation of the tangent line to the curve y  f(x) at the point where a  2 is y  4x  7, find f(2) and
f (2).
__________
101. Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
   
y sin2x  x cos 2y,  , 
2 4
__________
102. Find an equation of the tangent line to the curve 4x 2  3y 2  7 at the point (1, 1).
__________
103. If a tank holds 5000 gallons of water, and that water can drain from the tank in 40 minutes, then Torricelli's
2

t 
Law gives the volume V of water remaining in the tank after t minutes as V  5000 1   . Find the rate at
40 

which water is draining from the tank after 6 minutes.
__________
104. The quantity Q of charge in coulombs C that has passed through a point in a wire up to time t
(measured in seconds), is given by Q(t)  t 3  4t 2  4t  10.
Find the current when t 2s .
__________
105. The volume of a cube is increasing at a rate of 10 cm 3 /min . How fast is the surface area increasing when the
length of an edge is 30 cm .
__________
27
Name: ________________________
ID: A
106. Newton's Law of Gravitation says that the magnitude F of the force exerted by a body of mass m on a body of
GmM
mass M is F 
.
r2
Find
dF
5.
dr
__________
107. Differentiate.
g(x)  5sec x  tanx
__________
108. Find the derivative of the function.

 15
G(x)  7x  10 12  8x 2  3x  6


__________
1
sin4 t  where s is
7
measured in centimeter and t in seconds. Find the velocity of the particle after t seconds.
109. The displacement of a particle on a vibrating string is given by the equation s(t)  8 
__________
110. Find the given derivative by finding the first few derivatives and observing the pattern that occurs.
d 25
dx 25
sin x
_________
111. A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed
of 30 ft/s. At what rate is his distance from second base decreasing when he is halfway to first base? Round
the result to the nearest hundredth.
__________
28
Name: ________________________
ID: A
112. Find the given derivative by finding the first few derivatives and observing the pattern that occurs.
d 99
dx 99
sin x
_________
113. Differentiate the function.

3
f(t)   t  t 1 


__________
114. A television camera is positioned 4,600 ft from the base of a rocket launching pad. The angle of elevation of
the camera has to change at the correct rate in order to keep the rocket in sight. Also, the mechanism for
focusing the camera has to take into account the increasing distance from the camera to the rising rocket.
Let's assume the rocket rises vertically and its speed is 680 ft/s when it has risen 2,600 ft. If the television
camera is always kept aimed at the rocket, how fast is the camera's angle of elevation changing at this
moment? Round the result to the nearest thousandth.
__________
115. Find the derivative of the function.


y  3cos 1  sin 1 t 


_____________
116. Suppose that F(x)  f  g(x)  and g(17)  13, g (17)  15, f (17)  2, and f (13)  6.
Find F (17).
__________
117. Differentiate.
y
1
6
x  x3  1
__________
29
Name: ________________________
ID: A
118. The table lists the amount of U.S. cash per capita in circulation as of June 30 in the given year. Use a linear
approximation to estimate the amount of cash per capita in circulation in the year 2000.
__________
119. Use the linear approximation of the function f(x) 
7  x at a = 0 to approximate the number
7.1.
__________
120. Find an equation of the tangent line to the curve.
y
x
at  4, 0.2
x 6 
__________
121. The height (in meters) of a projectile shot vertically upward from a point 2 m above ground level with an
initial velocity of 24.5 m/s is h  2  24.5t  4.9t 2 after t seconds.
a) When does the projectile reach its maximum height?
b) What is the maximum height?
___________
122. A company makes computer chips from square wafers of silicon. It wants to keep the side length of a wafer
very close to 19 mm. The area is A(x). Find A(19).
__________
123. The volume of a cube is increasing at a rate of 10cm3 /min. How fast is the surface area increasing when the
length of an edge is 30 cm .
__________
30
Name: ________________________
ID: A
124. Newton's Law of Gravitation says that the magnitude F of the force exerted by a body of mass m on a body of
GmM
mass M is F 
.
r2
Find
dF
6.
dr
__________
125. Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
   
x sin 2y  y cos 2x,  , 
2 4
__________
126. Two carts, A and B, are connected by a rope 40 ft long that passes over a pulley (see the figure below). The
point Q is on the floor 10 ft directly beneath and between the carts. Cart A is being pulled away from Q at a
speed of 5 ft/s. How fast is cart B moving toward Q at the instant when cart A is 8 ft from Q?
__________
127. Find f (a).
f(x)  10  x  5x 2
__________
128. Find the given derivative by finding the first few derivatives and observing the pattern that occurs.
d 30
dx 30
sin x
__________
31
Name: ________________________
ID: A
129. Differentiate.



Y(u)   u 2  u 3   2u 5  u 3 



__________
130. Differentiate the function.

3
f(t)   t  t 1 


__________
131. The position function of a particle is given by s  t 3  3t 2  5t, t  0
When does the particle reach a velocity of 139 m/s?
__________
132. The height (in meters) of a projectile shot vertically upward from a point 2 m above ground level with an
initial velocity of 24.5 m/s is h  2  24.5t  4.9t 2 after t seconds.
a) When does the projectile reach its maximum height?
b) What is the maximum height?
___________


133. The mass of part of a wire is x  1  x  kilograms, where x is measured in meters from one end of the wire.


Find the linear density of the wire when x 4m .
__________
134. Find the equation of the tangent to the curve at the given point.
y
1  4sinx ,  0,1
__________
135. If a snowball melts so that its surface area decreases at a rate of 4 cm 2 /min, find the rate at which the
diameter decreases when the diameter is 39 cm.
__________
32
Name: ________________________
ID: A
136. Two cars start moving from the same point. One travels south at 27 mi/h and the other travels west at 50
mi/h. At what rate is the distance between the cars increasing 3 hours later? Round the result to the nearest
hundredth.
__________
137. The top of a ladder slides down a vertical wall at a rate of 0.15 m/s . At the moment when the bottom of the
ladder is 3 m from the wall, it slides away from the wall at a rate of 0.2 m/s . How long is the ladder?
__________
138. The altitude of a triangle is increasing at a rate of 3 cm/min while the area of the triangle is increasing at a
rate of 4 cm 2 /min. At what rate is the base of the triangle changing when the altitude is 10 cm and the area is
90 cm 2 .
__________
139. A water trough is 20 m long and a cross-section has the shape of an isosceles trapezoid that is 20 cm wide at
the bottom, 60 cm wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of
0.7 m 3 /min, how fast is the water level rising when the water is 45 cm deep? Round the result to the nearest
hundredth.
__________
140. A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the
dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 2 m/s how fast is the boat
approaching the dock when it is 3 m from the dock? Round the result to the nearest hundredth if necessary.
__________
141. The volume of a cube is increasing at a rate of 10 cm 3 /min . How fast is the surface area increasing when the
length of an edge is 30 cm .
__________
33
Name: ________________________
ID: A
142. Two carts, A and B, are connected by a rope 36 ft long that passes over a pulley (see the figure below). The
point Q is on the floor 14 ft directly beneath and between the carts. Cart A is being pulled away from Q at a
speed of 4 ft/s. How fast is cart B moving toward Q at the instant when cart A is 8 ft from Q? Round the
result to the nearest hundredth.
__________
143. The circumference of a sphere was measured to be 90 cm with a possible error of 0.5 cm. Use differentials to
estimate the maximum error in the calculated volume.
__________
144. Find the limit if g(x)  x 5 .
g(x)  g(2)
x 2
x2
lim
__________
145. Differentiate the function.
f(t) 
1 6
t  2t 4  t
3
__________
146. In this exercise we estimate the rate at which the total personal income is rising in the Richmond- Petersburg,
Virginia, metropolitan area. In 1999, the population of this area was 961,600, and the population was
increasing at roughly 9,400 people per year. The average annual income was $30,591 per capita, and this
average was increasing at about $1,300 per year (a little above the national average of about $1,225 yearly).
Use the Product Rule and these figures to estimate the rate at which total personal income was rising in the
Richmond-Petersburg area in 1999.
__________
34
Name: ________________________
ID: A
147. Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
   
x sin 2y  y cos 2x,  , 
2 4
__________
148. Refer to the law of laminar flow. Consider a blood vessel with radius 0.01 cm, length 3 cm, pressure
difference 3,500 dynes/ cm2 and viscosity 0.028 .
Find the velocity of the blood at radius r = 0.004.
__________
149. Differentiate.
g(x)  8sec x  tanx
__________
 

150. Find an equation of the tangent line to the curve y  sec x  9cos x at the point  ,  2.5 .
3

__________
151. Find the limit.
sinsin  
  0 sec 
lim
__________
152. The position function of a particle is given by s  t 3  4.5t 2  6t, t  0
When does the particle reach a velocity of 24 m/s?
__________
153. Find the given derivative by finding the first few derivatives and observing the pattern that occurs.
d 89
dx 89
sin x
__________
35
Name: ________________________
ID: A
154. If an equation of the tangent line to the curve y  f(x) at the point where a  2 is y  4x  5, find f(2) and
f (2).
__________
155. The height (in meters) of a projectile shot vertically upward from a point 2 m above ground level with an
initial velocity of 24.5 m/s is h  2  24.5t  4.9t 2 after t seconds.
a) When does the projectile reach its maximum height?
b) What is the maximum height?
___________
156. Find the first and the second derivatives of the function.
G(r) 
r 5 r
__________

d  h(x)  



157. If h(2)  7 and h (2)  2, find
dx  x  


x2
__________
158. Find a third-degree polynomial Q such that Q (1) = 2, Q (1) = 7, Q (1) = 14, and Q (1) = 18.
__________
159. Calculate y .
cos  xy   x 2  y
__________
160. A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed
of 28 ft/s. At what rate is his distance from second base decreasing when he is halfway to first base? Round
the result to the nearest hundredth.
__________
36
ID: A
Derivatives Practice - Stewart
Answer Section
MULTIPLE CHOICE
1. ANS:
NOT:
2. ANS:
NOT:
3. ANS:
NOT:
4. ANS:
NOT:
5. ANS:
NOT:
6. ANS:
NOT:
7. ANS:
NOT:
8. ANS:
NOT:
9. ANS:
NOT:
10. ANS:
NOT:
11. ANS:
NOT:
12. ANS:
NOT:
13. ANS:
NOT:
14. ANS:
NOT:
15. ANS:
NOT:
16. ANS:
NOT:
17. ANS:
NOT:
18. ANS:
NOT:
19. ANS:
NOT:
20. ANS:
NOT:
E
Section 2.3
E
Section 2.5
A
Section 2.9
A
Section 2.3
B
Section 2.7
C
Section 2.7
B
Section 2.7
C
Section 2.6
C
Section 2.4
C
Section 2.5
A
Section 2.3
D
Section 2.8
A
Section 2.5
E
Section 2.6
B
Section 2.9
B
Section 2.6
B
Section 2.8
D
Section 2.9
D
Section 2.5
B
Section 2.7
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
1
ID: A
21. ANS:
NOT:
22. ANS:
NOT:
23. ANS:
NOT:
24. ANS:
NOT:
25. ANS:
NOT:
26. ANS:
NOT:
27. ANS:
NOT:
28. ANS:
NOT:
29. ANS:
NOT:
30. ANS:
NOT:
31. ANS:
NOT:
32. ANS:
NOT:
33. ANS:
NOT:
34. ANS:
NOT:
35. ANS:
NOT:
36. ANS:
NOT:
37. ANS:
NOT:
38. ANS:
NOT:
39. ANS:
NOT:
40. ANS:
NOT:
41. ANS:
NOT:
42. ANS:
NOT:
43. ANS:
NOT:
B
Section 2.5
C
Section 2.3
C
Section 2.6
D
Section 2.5
C
Section 2.7
A
Section 2.9
D
Section 2.9
D
Section 2.1
D
Section 2.8
B
Section 2.8
C
Section 2.1
B
Section 2.8
C
Section 2.8
D
Section 2.8
A
Section 2.7
A
Section 2.4
A
Section 2.7
C
Section 2.8
B
Section 2.3
D
Section 2.3
D
Section 2.9
C
Section 2.9
D
Section 2.1
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
2
ID: A
44. ANS:
NOT:
45. ANS:
NOT:
46. ANS:
NOT:
47. ANS:
NOT:
48. ANS:
NOT:
49. ANS:
NOT:
50. ANS:
NOT:
51. ANS:
NOT:
52. ANS:
NOT:
53. ANS:
NOT:
54. ANS:
NOT:
A
Section 2.3
D
Section 2.1
A
Section 2.5
B
Section 2.7
B
Section 2.9
D
Section 2.3
D
Section 2.3
D
Section 2.4
C
Section 2.6
C
Section 2.7
A
Section 2.5
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Numerical Response
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
PTS: 1
DIF:
Medium
MSC: Multiple Choice
MULTIPLE RESPONSE
55. ANS:
NOT:
56. ANS:
NOT:
A, D
Section 2.3
A, D
Section 2.5
NUMERIC RESPONSE
57. ANS: f(2)  3
f (2)  4
PTS:
NOT:
58. ANS:
1
DIF:
Section 2.1
 1, 6 ,  2, 21

 

Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.3
59. ANS: y  2x  1
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.5
DIF:
Medium
MSC: Numerical Response
3
ID: A
60. ANS: g (x)  7x 6 cos x   x 7 sin x 
PTS: 1
NOT: Section 2.4
DIF:
Medium
MSC: Numerical Response
61. ANS: f (x)  2xg(x)  x 2 g (x)
PTS: 1
NOT: Section 2.3
62. ANS: a) 2.5 s
DIF:
Medium
MSC: Numerical Response
DIF:
Medium
MSC: Numerical Response
b) 32.625 m
PTS: 1
NOT: Section 2.7
1
63. ANS: y  x
2
PTS: 1
DIF: Medium
NOT: Section 2.6

1  x sin x  cos x

64. ANS: y   
2 
x

MSC: Numerical Response






PTS: 1
NOT: Section 2.5
65. ANS: 8
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.7
DIF:
Medium
MSC: Numerical Response
66. ANS: y   
2

 

 2 
 1  t 2   1   sin1 t   

 

 
PTS: 1
DIF: Medium
NOT: Section 2.5
1
x  4  0.2
67. ANS: y 
200
MSC: Numerical Response
PTS: 1
NOT: Section 2.1
68. ANS: 5 m
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.8
DIF:
Medium
MSC: Numerical Response
4
ID: A
69. ANS: 80
PTS: 1
NOT: Section 2.4
70. ANS: 32
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.7
DIF:
Medium
MSC: Numerical Response
Medium
MSC: Numerical Response
71. ANS: y  
1  y 4  2xy
4xy 3  x 2  3
PTS: 1
NOT: Section 2.6
DIF:
72. ANS: 33  x 2 , 63  x 3
PTS: 1
NOT: Section 2.3
73. ANS: cos x
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.4
74. ANS: 465
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.6
4
75. ANS: cm2 / min
3
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.8
36t
76. ANS:

2
 3  t 2 


DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.3
77. ANS: f(2)  1
DIF:
Medium
MSC: Numerical Response
f (2)  4
PTS: 1
DIF: Medium
MSC: Numerical Response
NOT: Section 2.1

 


78. ANS: 6x 2  x 4  2x    2x 3  1  4x 3  2

 


PTS: 1
NOT: Section 2.3
DIF:
Medium
MSC: Numerical Response
5
ID: A
79. ANS: y   
3

 

 2 
 1  t 2   1   sin1 t   

 

 
PTS: 1
NOT: Section 2.6
80. ANS: 9
DIF:
Medium
MSC: Numerical Response
PTS: 1
DIF:
NOT: Section 2.1
81. ANS: f (x)  2g(x)g (x)
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.3
82. ANS: 24.75
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.5
83. ANS: 8
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.7
84. ANS: 2.75
DIF:
Medium
MSC: Numerical Response
PTS: 1
DIF:
NOT: Section 2.3
dy
7cos x  1

85. ANS:
dx 7  cos x 2
Medium
MSC: Numerical Response
PTS: 1
DIF: Medium
NOT: Section 2.4
dy
 cos x   2sinx 
86. ANS:
dx
MSC: Numerical Response
PTS: 1
DIF:
NOT: Section 2.4

 
87. ANS: y  6x  3 1  
2

Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.4
88. ANS: 0.1
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.5
DIF:
Medium
MSC: Numerical Response
6
ID: A


89. ANS: dy   4x 3  5 dx


PTS: 1
DIF: Medium
NOT: Section 2.9
   
  3



 2 n, 5
90. ANS:     2 n,7 , 
 2 
  2



MSC: Numerical Response
PTS: 1
NOT: Section 2.3
3
91. ANS: y  x 
4
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.6
4
92. ANS: f (2)  
27
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.5
93. ANS: y  2x  1
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.5
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.5
95. ANS: cos x
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.4
96. ANS: 5 m
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.8
97. ANS: a) 2.6 s
DIF:
Medium
MSC: Numerical Response
PTS: 1
DIF:
NOT: Section 2.7
98. ANS: tanx  tan y 
Medium
MSC: Numerical Response
Medium
MSC: Numerical Response
94. ANS: 32x  1 5/2
b) 34.624 m
PTS: 1
NOT: Section 2.6
DIF:
7
ID: A
99. ANS: y   
1

 

 2 
 1  t 2   1   sin1 t   

 

 
PTS: 1
NOT: Section 2.5
100. ANS: f(2)  1
DIF:
Medium
MSC: Numerical Response
DIF:
Medium
MSC: Numerical Response
PTS: 1
DIF:
NOT: Section 2.6
4
7
102. ANS: y   x 
3
3
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.1
103. ANS: 212.5
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.1
104. ANS: 0
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.7
4
105. ANS: cm2 / min
3
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.9
2GmM
106. ANS:
125
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.7
DIF:
Medium
MSC: Numerical Response
f (2)  4
PTS: 1
NOT: Section 2.1
1
101. ANS: y  x
2
107. ANS: g (x)  5sec x  tanx   sec 2 x
PTS: 1
NOT: Section 2.4
DIF:
Medium
MSC: Numerical Response
8
ID: A

 15

 14
108. ANS: 847x  10 11  8x 2  3x  6  157x  10 12  8x 2  3x  6 16x  3




PTS: 1
DIF:
NOT: Section 2.5
4
cos 4 t 
109. ANS:
7
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.5
110. ANS: cos x
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.4
111. ANS: 13.42 ft/s
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.8
112. ANS: cos x
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.4
DIF:
Medium
MSC: Numerical Response

 2 t2  1
113. ANS: f (t)  3 t 2  1


t4
PTS: 1
NOT: Section 2.5
114. ANS: 0.112 ft/s
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.8
DIF:
Medium
MSC: Numerical Response
115. ANS: y   
3




 2 
 1  t 2   1   sin1 t   

 

 
PTS: 1
NOT: Section 2.5
116. ANS: 90
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.5
DIF:
Medium
MSC: Numerical Response
9
ID: A


  6x 5  3x 2 


117. ANS: y  
2
 6

 x  x 3  1 


PTS: 1
NOT: Section 2.5
118. ANS: 1565
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.9
119. ANS: 2.66
DIF:
Medium
MSC: Numerical Response
PTS: 1
DIF: Medium
NOT: Section 2.9
1
x  4  0.2
120. ANS: y 
200
MSC: Numerical Response
PTS: 1
NOT: Section 2.1
121. ANS: a) 2.5 s
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.7
122. ANS: 38
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.7
4
123. ANS: cm2 / min
3
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.8
2GmM
124. ANS:
216
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.7
3
125. ANS: y  x 
4
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.6
DIF:
Medium
MSC: Numerical Response
b) 32.625 m
10
ID: A
126. ANS: 3.36
PTS: 1
NOT: Section 2.8
127. ANS: 1  10a
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.3
128. ANS: sinx
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.4
DIF:
Medium
MSC: Numerical Response
Medium
MSC: Numerical Response
129. ANS: Y (u)  6u 2  4u  1
PTS: 1
NOT: Section 2.3
DIF:
 2
 2 t2  1





f
(t)

3
t

1
130. ANS:



t4
PTS: 1
NOT: Section 2.5
131. ANS: 8
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.1
132. ANS: a) 2.5 s
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.7
133. ANS: 4 kg/m
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.9
134. ANS: y  2x  1
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.5
2
135. ANS:
39
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.8
DIF:
Medium
MSC: Numerical Response
b) 32.625 m
11
ID: A
136. ANS: 56.82
PTS: 1
NOT: Section 2.8
137. ANS: 5 m
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.8
138. ANS: 4.6
DIF:
Medium
MSC: Numerical Response
PTS: 1
DIF:
NOT: Section 2.8
139. ANS: 6.25 cm/min
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.8
140. ANS: 2.11
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.8
4
141. ANS: cm2 / min
3
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.9
142. ANS: 2.8
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.8
143. ANS: 205
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.9
144. ANS: 80
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.4
DIF:
Medium
MSC: Numerical Response
Medium
MSC: Numerical Response
Medium
MSC: Numerical Response
145. ANS: f (t)  2t 5  8t 3  1
PTS: 1
DIF:
NOT: Section 2.3
146. ANS: $1,537,635,400
PTS: 1
NOT: Section 2.3
DIF:
12
ID: A
147. ANS: y  x 
3
4
PTS: 1
NOT: Section 2.6
148. ANS: 0.88
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.7
DIF:
Medium
MSC: Numerical Response
149. ANS: g (x)  8sec x  tanx   sec 2 x
PTS: 1
NOT: Section 2.3
DIF:
Medium
MSC: Numerical Response

 
150. ANS: y  6.5 3  x    2.5

3
PTS: 1
NOT: Section 2.4
151. ANS: 0
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.4
152. ANS: 5
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.1
153. ANS: cos x
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.4
154. ANS: f(2)  3
DIF:
Medium
MSC: Numerical Response
DIF:
Medium
MSC: Numerical Response
f (2)  4
PTS: 1
NOT: Section 2.1
155. ANS: a) 2.5 s
b) 32.625 m
PTS: 1
DIF: Medium
MSC: Numerical Response
NOT: Section 2.7
1
1
1
4 9/5
r
156. ANS: r 1/2  r 4/5 ,  r 3/2 
2
5
4
25
PTS: 1
NOT: Section 2.3
DIF:
Medium
MSC: Numerical Response
13
ID: A
157. ANS: 2.75
PTS: 1
NOT: Section 2.3
DIF:
Medium
MSC: Numerical Response
158. ANS: Q  3x 3  2x 2  2x  1
PTS: 1
DIF: Medium
NOT: Section 2.3
2x  y  sin xy  


159. ANS: y  


1  x  sin xy  


MSC: Numerical Response
PTS: 1
NOT: Section 2.6
160. ANS: 12.52 ft/s
DIF:
Medium
MSC: Numerical Response
PTS: 1
NOT: Section 2.8
DIF:
Medium
MSC: Numerical Response
14