Trig/Math Anal
HW NO.
IN-1
IN-2
IN-3
IN-4
IN-5
IN-6
IN-7
IN-8
IN-9
IN-10
Name_______________________No_____
SECTIONS
ASSIGNMENT
Practice Set B #1-43 odd, 44
Practice Set C #1-33 odd
Practice Set D
Practice Set E
Practice Set F #1-11
Practice Set G #1-19 odd
Practice Set G #2-18 even
Practice Set H
Practice Set J
Practice Set K
√
DUE
Test Date (no graphing calculators allowed):
Practice Set A: Derivatives Review
Find the first derivative.
4
1. f x  2 x 5
2. f x  2 x 2  3
4.
bg
f bg
x x b
3x  2g
3
bg 5 x4 x 1
c h
f bg
x e
f bg
x  xe  e  x
7. f x 
10.
13.
5.
8.
x 2 7 x
x
2x
16. y 
3
ln x
x5
14.
17.
c hb g
y  lnb
ln xg
f bgc
x  e  4 xh
x ln x  x
f bg
x 
x 1
1
f bg
x  e
e
20.
22.
23.
28.
31.
2
1
x
x
bg
81914768 Page 1
10
3x
34. f x  ln
4 x
bg ex
1 x
(Simplify)
1 x
x 7
4
18.
4
21.
2
24.
26. y  3 e3 x  x
27.
bg e
f bg
x e 
32.
x
bg
ex
35. f x  x 3 ln x  4 x
4
bg
e
f bg
x 
1 e
Fx I
y  lnGJ
H2 K
y  e lnb
4 x  2g
y  e  lnb
5x  2g
f bg
x  5c
lnb
4 x  5g
h
f bg
x e
x 1
x
15.
x
29. f x  ln x  1  x 2
x
12. f x  e x  3x
5
3x
3
3
9. f x 
bg
f bgc
x  e  1h
y  lnc
x e h
yb
ln xg
f bg
x  lnc
x  5x h
11. f x  e
19. y  ln x 2  3x 9 x  2
25.
6.
2
2
2
bg c3x  4xh
f bg
x  2x c
4x h
3. f x 
4
3
2
bg c h
x
f bg
x 
3x
f bg
x x e
j
30.
x
5x
4x
4
1x
2
 e 3 x
3x
 e 3 x
(Simplify numerator of answer)
5xe 2 x
36. f x 
3x  x 2
bg ee
33. f x 
bg
3x
bgc hc h
f bg
x  e lnc
x  3x  2 h
y  xb
ln x g 2 x ln x  2 x
  5x  3  5  8x  

  7  3x 

5x
3
x
40. f x  e  x  xe
38. f x  4 x 3  3x e4 x  3
43.
44.
4
37. f  x   ln 
2
bg
f bg
x  lnc
lnb
ln xg
h
2x
47. y  e 2 x 
L
xc
x  1hO
M
P
y  ln
M
N2 x  1 P
Q
50. f x  3
2
2
2
e 2 x
x3
5x  2
3x  1
bg
3
52. f ( x)  ln(ln(5x 2  3x))
bg
Practice Set B: Integration
Find each of the following:
1.  4xdx
 6x dx
7.  (2 z  3)dz
10.  (t  2t )dt
13.  (4 z  3 z  2 z  6)dz
16.  t dt
19.  (15 x x  2 x )dx
22.  (56t  18t )dt
3
4.
2
3
2
1
4
5
2
25.
 1
  y
3
7
2

1 
 dy
y 

28.  (8 x 3  4 x 1 )dx
31.
 3e
.2 x
dx
9

34.    3e .4 x  dx
x

81914768 Page 2
bg ec
39. f x  ln ln 3x 2  7 x  2
bg c h
42. f x  ln x 2  4
e 2 x
x3
e x  e x
48. y  x
(Simplify
e  e x
answer)
ln x
51. f x 
2
1  ln x
45. y  e 2 x 
54. Find the maximum value of
f x  x 2 e  x on 0  x  4 .
Hint: Take the first derivative,
set=0, solve… Note: you just
graphed the function.
bg
bg
 8xdx
5.  6dk
8.  (3x  5)dx
11.  (t  4t  5)dt
14.  (12 y  6 y  8 y  5)dy
17.  (u  u )du
20.  ( x  x )dx
2
3
bg 1x
2
1
2
3
2
1
2
 12
 1 
dz
2 

1 

26.   u  2  du
u 

 5t dt
6.  2dy
9.  ( x  6 x) dx
12.  (5 x  6 x  3)dx
15.  5 zdz
18.  (4 v  3v )dv
21.  (10u  14u )du
3.
2
2
2
3
2
3
2
  z
24.
  x
29.
 e dt
 4 e
30.
e
33.
  x  4e
2t
.2 v
dv
1  2t 3
35. 
dt
t
5
2
 4
dx
3 

27.  (9t 2  2t 1 )dt
23.
32.
4
56. If f x  ln x then f ' x 
2.
hj
bg b g
53. Graph y  x 2 e  x for
1  x  5
Prove the following (check your notes).
55. If f x  e x then f ' x  e x
bg
4
2
bg 1  lnblnxxg
46. f x 
49.
41.
5
3 y
3
1
dy
.5 x

 dx

2 y 2  3y2
dy
36. 
y
 (e  4u )du
 (2 y  1) dy
2u
37.
 (v
38.
2
40.
 e3v )dv
x 1
dx
3
x

41.
2
43. Find an equation of the curve whose
2
tangent line has a slope of f '( x)  x 3 , given
that the point (1, 53 ) is on the curve.
 ( x  1)
39.
2
dx
1 2 3 z
 3 z dz
44. The slope of the tangent line to a curve is
given by f '( x)  6 x 2  4 x  3 . If the point
(0, 1) is on the curve, find an equation of the
curve.
42.
Practice Set C: Definite Integrals
Integrate and evaluate.
1
1.
2
2
 ( x  x )dx
2.
0
7.
 e dx
x
5.
a
b
2
 3t dt
8.
6.
11.
9.
0
1
14.
t dt
0
  x   dx
1
x
1

1
10 3
17
2
1
1

 (ax  x )dx
e
3
 4t dt
1
  x  1x  dx
 x 4 )dx
0
a
e
13.
 e dt
0
2
a
t
b
 (x
1
b
a
10.
3.
1
b
4.
1
2
 ( x  x)dx

12.
xdx
3
xdx
0
12 2
13
t dt
0
Find the area under the graph on the interval indicated:
15. y  x3 ; 0, 2
16. y  x4 ; 0,1
17. y  x2  x  1;  2,3
18. y  2  x  x2 ;  2,1
19. y  5  x2 ;  1, 2
20. y  ex ;  2,3
21. y  e x ;  1,5
22. y  2 x  x12 ; 1, 4
23. y  2 x  x12 ; 1,3
4  x 2 , if x  0
25. f ( x)  
on  2,3
4, if x  0
 x 2 , if x  1
24. f ( x)  
on  2,3
1, if x  1
Integrate.
2
26.
29.
 (4 x  3)(5x  2)dx
2
3
t t
dt
3
t
1
1 2
x
3
dx
x2  4
3 x  2 dx
28.

33.
t3 1
0 t  1 dt
4.
zcx
3
h
2
z
8
1
81914768 Page 3
3 y
y
2
3
1
3
dy
t 1
dt
t
4
31.

3.
zc
1
 3x  5 dx
2
3
0
Practice Set D: Definite Integrals/Area
Integrate and evaluate.
1.
 (t  1) dt
9
5
30.
1
5
32.
 (t  3)(t  3)dt
1
x  
1
5
27.
2.
5.
zd5y y  33 y idy
IdA
2e
 J
zFG
H AK
4
1
3
2
 .1 A
5
1
h
5n 2  n 3 dn
Graph, find the area between the x-axis and the function over the indicted interval. Check to see if
the graph crosses the x-axis on the given interval.
6. f x  9  x 2 [0, 5]
7. f x  x 2  4 x [-4, 6]
x  2y  2
8. Find the area formed by the given equations: y  x  1
Hint:
Part A  Part B
bg
bg
z z
2x  y  7
Practice Set E: Area
Graph, find the points of intersection and find the area.
y  x3
y  x 2  3x
1.
2. y  5x  17
y  x 1
y  x2  2x
3.
yx
y  x 1
y  x6
5.
4. y  2 x
yx
Practice Set F: Review
Integrate/evaluate.
1.  (4 x 4  6 x 2  9)dx
y  4  x2
y  4 x  4
3
 5

4.   3  4 x3  dx
x

4 x3  3
2.
 4e dx
3.
 x dx
5.
4 x 2  11x  3
 x  3 dx
1
6.
  2 x  5 dx
x
3
x6
9.
 3 x2
4 x dx
Graph, find the points of intersection and find the area.
y  85 x  238
y  x2  4x  5
10.
11. y  2 x  16
y  2 x 2  6 x  1
7.
25
dx
8.
6
2
3
  5  x x dx
3
2
13
y  101 x  10
Integrate using substitution.
9
dt
12. 
2  5t
13.
Practice Set G: Integration by Substitution
Integrate/evaluate.
1.  4(2 x  3) 4 dx
2.  (4t  1)3 dt
4.

3dx
3x  5
5.
 z z  5dz
10.  5e dg
13.  (1  t )e dt
7.
2
.3 g
2 t t 2
81914768 Page 4
 (x
2
2x  2
dx
 2 x  4)4
 r ( r  2)dr
11.  3x e dx
14.  ( x  1)e
dx
2
8.
2 2 x3
2
x3 3 x
B3  1
 (2 B
4
3
 8B) 2
dB
3.
6.
2dm
 (2m  1)
3
6 x 2 dx
 (2 x
3
 (4e
12.  re
9.
3
 7) 2
2p
r2
1
)dp
dr
ez
15.  2 dz
z
e y
16. 
dy
2 y
3

19.
1
17.
5x2
5x
3
 2
3
8
 1  3x dx
2
2 x2

18.
3
1  3 x  1
2
dx
20. Graph, find the points of intersection; find the
area.
x  2 y  10
dx
y   32 x  9
x  2y  2
Graph, find the area between the function and the x-axis on the given interval.
21. f ( x)  x3 on  2, 2
22. f ( x)  9  x2 on  5, 4
Practice Set H: Multiple Integrals
Integrate and evaluate.
6 2
1.
1 3
2
  10xy dxdy
2.
3 1
  (x  y
1 x
3.
0 1
2 x
4.
  ( x  y )dydx
0 x2
1 3 2
1 x
2
5.
)dydx
  xy dydx
2
0 x
0 0
  ( x  y)dydx
6.
   (2 x  3 y  z )dxdydz
0 1 1
2
7. Graph, find the area between x-axis over the
indicated interval. Check to see if the graph
crosses the x-axis on the given interval.
f ( x)  3x  x2 ;  2,5
8. Graph, find the points of intersection and
find the area.
y  x2  6x
y  x
Practice Set J: Review
Integrate/evaluate.
2 x x y
1 1 x 2
1.

0
(1  y  x 2 )dydx
 
5.
x3  8
0 x  2 dx
7.
x
( y  2 z )dzdydx
3.
x4
4 x dx
Integrate by substitution.
6.  (2 x  5)6 dx

1
4.
2
( x 3  2) 4 dx
ln(3  x)
4
6x
 x 2  4 dx
10.

dx
8.
x2
 ( x3  5)2 dx
11.
(3  x)
Graph, find the points of intersection and find the area.
y4
y   x 2  3x  5
13.
12. x  1
y  2x2  4x  2
yx
Practice Set K: Review
Integrate/evaluate
4
3
0
1
2
1 

1.   x  2  dx
2.  x 3  x 3 dx
3.  (2  x) xdx
x 
0
2 
1
Integrate by substitution

81914768 Page 5
x (10 x 2  3)dx
1
0 0 0
0
9
9.
4
2.

 xe
x2
dx
1
4.
x  x2
 3 dx
8 2 x
2
5.
( x  1)dx
1
3
2
 x 4  x dx
6.
0

x2  2 x  1
0
Integrate and evaluate
2 4
7.
2
2
  ( x  2 y  1)dxdy
3 2 1
2
2 2 y y
8.
1 0
 
9.
3 ydxdy
   ( x  y  z )dxdydz
0 0 0
0 3 y2 6 y
Graph, find the points of intersection and find the area
x  2y  2
 x 2  5, 3  x  0
f ( x)  
11.
2
10. y  x  1
5  x , 0  x  2
2x  y  7
Practice Set L: Review
Integrate/evaluate
1
8
4 y
(3 x 2  1) 2
2
3
dx
1.  x  x dx
3. 
2.   ( x  2 y )dxdy
x2
0
1
1


0
2 x x y
4.
   ( y  2 z)dzdydx
0 0 0
Integrate by substitution
x
dx
6.  2
7.
x 4
2
y
4
5.

x (10 x  3)dx
1
(ln x) 2
 x dx
10. Graph, find the points of intersection and
find the area.
y   12 x  4

x2
16
e
4
x
1 4 x3 dx
2  x3
11. Graph, find the area between the function
and the x-axis on the given interval.
f ( x)  1  34 x on  2, 4
8.
4
dx
9.
y  43 x  7
y   85 x  95
Practice Set M: Integration Application Problems
Cost--Find the cost function for each of the following marginal cost functions.
1
1. C' x  4 x  5 , fixed cost is $8
2. C ' x  x  2 , 2 units cost $5.50
x
.01 x
1
3. C ' x .03e , fixed cost is $8
4. C ' x   2 x , 7 units cost $58.40
x
5. Profit: The marginal profit of a small fast-food stand is given by P' x  2 x  20 where x is the
sales volume in thousands of hamburgers. The “profit” is -$50 when no hamburgers are sold. Find
the profit function.
6. Seat Belt Usage: In Sacramento County in California the use of seat belts has risen steadily since
the enactment of a seat belt law in 1986. The rate of change (in %) of drivers using seat belts in
. x 2  6.86 x  3.24 . In
year x, where 1985 corresponds to x=0, is modeled by f ' x .116 x 3  1803
1985 (year 0), 26% of drivers used seat belts.
a. Find the function that gives the percent of drivers using seat belts in year x.
b. According to this function, what percent of drivers used seat belts in 1993?
bg
bg
bg
bg
bg
bg
81914768 Page 6
7. Vehicle Related Deaths: Vehicle-related deaths in Sacramento County have declined since 1986
when the California seat belt law was enacted. The rate of change in deaths per 100 million miles
of vehicle travel is modeled by g ' x  .00156 x 3 .0312 x 2 .264 x .137 where x=0 corresponds to
1985 and so on. There were 2.4 deaths per 100 million miles driven in 1985.
a. Find the function giving the number of deaths per 100 million miles in year x.
b. How many deaths were there in 1986? In 1990?
8. Velocity: For a particular object, a t  t 2  1 and v 0  6 . Find v t .
2
9. Distance: Suppose v t  6t 2  2 and s 1  8 . Find s t .
t
10. Time: An object is dropped from a small plane flying at 6400 feet. Assume that a t  32
feet per second per second and v 0  0 , find s t . How long will it take the object to hit the
ground?
11. Distance: Suppose a t  18t  8 , v 1  15 , and s 1  19 . Find s t .
15
12. Distance: Suppose a t 
 3e  t , v 0  3 , and s 0  4 . Find s t .
2 t
Practice Set N: Integration Application Problems (Substitution)
Integrate by substitution.
2dm
2x  2
3. r r 2  2 dr
1.
2.
dx
3
4
2m  1
x2  2x  4
bg
bg
bg
bg
bg
bg
4.
zb
z
bg
bg
g
re  r dr
2
5.
bg
bg
bg
bg
bg
bg
zc
zb
bg
bg
bg
bg
h
g
p p  1 dp
5
6.
z
z
4r 8  r dr
(use double substitution)
(use double substitution)
7. Revenue: Suppose the marginal revenue in dollars from the sale of x jet planes is
bg c
h
R' x  2 x x 2  50
2
a. Find the total revenue function if the revenue from 3 planes is $206, 379.
b. How many planes must be sold for a revenue of at least $450,000?
8. Cost: A company has found that the marginal cost of a new production line (in thousands) is
60 x
C' x  2
, where x is the number of years the line is in use.
5x  e
a. Find the total cost function for the production line. The fixed cost is $10,000.
b. The company will add the new line if the total cost is reduced to $20,000 within 5
years. Should they add the new line?
9. Profit: The rate of growth of the profit (in millions of dollars) from a new technology is
bg
bg
approximated by P' x  xe  x where x represents time measured in years. The total profit in the
third year that the new technology is in operation is $10,000.
a. Find the total profit function.
b. What happens to the total amount of profit in the long run?
10. Cell Growth: Under certain conditions, the number of cancer cells N t at time t increases at
bg
2
bg
a rate N ' t  Ae , where A is the rate of increase at time 0 (in cells per day) and k is a constant.
a. Suppose A=50, and at 5 days, the cells are growing at a rate of 250 per day. Find a
formula for the number of cells after t days, given that 300 cells are present at t=0.
b. Use your answer from part a to find the number of cells present after 12 days.
81914768 Page 7
kt
11. Find the area enclosed by these functions: y  x 3  x 2  x  1, y  2 x 2  x  1
Practice Set P: Integration Application Problems (Definite)
Find the area on the given interval between the function and the x-axis.
1
1. f x  9  x 2 , [0, 6]
3. f x  x 2  2 x , [-1, 2]
2. f x  , [1, e]
x
4. Profit: A small company of science writers found that its rate of profit (in thousand of dollars)
bg
bg
bg
bgb gc
after t years of operation is given by P' x  3t  3 t 2  2t  2
h
1
3
a. Find the total profit in the first three years.
b. Find the profit in the fourth year of operation.
5. Worker Efficiency: A worker new to a job will improve his efficiency with time so that it takes
him fewer hours to produce an item with each day on the job, up to a certain point. Suppose the
rate of change of the number of hours it takes a worker is given by H ' x  20  2 x
a. What is the total number of hours required to produce the first 5 items?
b. What is the total number of hours required to produce the next 5 items?
6. Pollution: Pollution from a factory is entering a lake. The rate of concentration of the pollutant
5
at time t is given by P' t  140t 2 , where t is the number of years since the factory started
introducing pollutants in the lake. Ecologists estimate the lake can accept a total level of pollution
of 4850 units before all the fish life in the lake ends. Can the factory operate for 4 years without
killing all the fish in the lake?
7. Age Distribution: The 1990 U.S. census gives us an age distribution which is approximately
given (in millions) by the function f x  32  4.45x .88 x 2 , where x varies from 0 to 9 decades.
The population of a given age group can be found by integrating this function over the interval for
that age group.
a. Find the integral over the interval [0, 9]. What does this integral represent?
b. Baby boomers are those born between 1945 and 1965, that is, those in the age
range of 2.5 to 4.5 decades in 1990. Find the number of baby boomers.
8. Income Distribution: Based on 1990 census data, an approximate income distribution for the
U.S. is given by the function f x  15.6.02 x .154 x 2 , where x is annual income in units of
$10,000, .5  x  10 . For example, x .5 represents an annual income of $5000. The percent of
the population with an income in a given range can be found by integrating this function over the
range. Find the percentage of the population with an income between $25,000 and $50,000.
9. Oil Consumption: Suppose that the rate of consumption of a natural resource is c' t  ke rt .
Here t is time in years, r is a constant, and k is the consumption in the year when t=0. In 1992, an
oil company sold 1.2 billion barrels of oil. Assume that r .04
a. Find the amount of oil that the company will sell in the next ten years.
b. The company has about 20 billion barrels of oil in reserve. To find the number of years
bg
bg
bg
bg
bg
that this amount will last, solve the equation
Integrate using substitution.
9
dt
10.
2  5t
z
11.
z
T
0
12
. e.04 t dt  20
1 IF 1 I
1 J
dr
zFG
Hr  rJ
KG
H
r K
2
12.
Practice Set Q: Integration Application Problems (Area)
Find the area on the given interval between the function and the x-axis.
81914768 Page 8
zc
B3  1
2 B4  8B
h
3
2
dB
bg
bg
1. f x  e x  1 , [-1, 2]
2. f x  4  x 2 , [0, 3]
3. Net Savings: Suppose a company wants to introduce a new machine that will produce a rate of
annual savings in dollars given by S x  150  x 2 where x is the number of years of operation of
11
the machine, while producing rate of annual costs in dollars of C x  x 2  x
4
a. For how many years will it be profitable to use this new machine?
b. What are the net total savings during the first year of use of the machine?
c. What are the net total savings over the entire period of use of the machine?
4. Profit: De Win Enterprises had an expenditure rate of E x  e.1x dollars per day and an income
bg
bg
bg
bg
rate of I x  98.8  e dollars per day on a particular job, where x was the number of days from
the start of the job. The company’s profit on that job will equal total income less total
expenditures. Profit will be maximized if the job ends at the optimum time, which is the point
where the two curves meet. Find the following.
a. The optimum number of days for the job to last
b. The total income for the optimum number of days
c. The total expenditures for the optimum number of days
d. The maximum profit for the job
5. Net Savings: A factory at Harold Levinson Industries has installed a new process that will
t
produce an increased rate of revenue (in thousands of dollars per year) of R t  104.4e 2 , where
t is time measured in years. The new process produces additional costs (in thousands of dollars
t
per year) at the rate of C t .3e 2 .
a. When will it no longer be profitable to use this new process?
b. Find the net total savings.
6. Producer’s Surplus: Find the producers’ surplus if the supply function for pork bellies is given by
5
3
S q  q 2  2q 2  50 . Assume supply and demand are in equilibrium at q  16 .
7. Consumers’ Surplus: Find the consumers’ surplus if the demand function for grass seed is given
100
by D q 
, assuming supply and demand are in equilibrium at q  3 .
2
3q  1
.1 x
bg
bg
bg
bg b g
Integrate by substitution.
8.
ze
jb g
zb1 ln xgdx
2
x 2  12 x x  6 dx
9.
Practice Set R: Integration Application Problems (Review)
Integrate/evaluate.
1
2
4
1.
x 2  3x 3 dx
dx
2.
x3
2
3x
4. xe 3 x dx
dx
5.
2
x 1
7.
10.
ze
z
zc
z
81914768 Page 9
x 2  5x
6
1
j
hb2 x  5gdx
4
5 4x
e dx
2
8.
z
z
z
z
x3
4
dx
e3x
2
4 3x  10 x
dx
11.
1
x
x
3.
6.
9.
z
zc
z
3e2 x dx
x 2 dx
h
x3  5
6
1
8x 1dx
4
Find the area of the region enclosed by each group of curves.
14. f x   21 x  7; g x  2 x  1; h x  x  5
12. f x  5  x 2 , g x  x 2  3
bg
bg
bg
x  5  x , gbg
x  x  3, x  0, x  4
13.
15. f bg
16. Cost: Find the cost function if the marginal cost function is C' bg
x  3 2 x  1 ; 13 units cost
bg
f bg
x x
2
bg
 4 x; gbg
x  x6
2
2
$270
17. Utilization of Reserves: A manufacturer of electronic equipment requires a certain rare metal.
He has a reserve supply of 4,000,000 units that he will not be able to replace. If the rate at which
the metal is used is given by f ' t  100,000e.03t , where t is the time in years, how long will it be
before he uses up the supply? (Hint: Find an expression for the total amount used in t years and
set it equal to the know reserve supply)
18. Sales: The rate of change of sales of a new brand of tomato soup (in thousands per month) is
given by S ' x  x  2 , where x is the time in months that the new product has been on the
market. Find the total sales after 9 months.
19. Productivity: The function defined by f ' x  2.158e.0198 x approximates marginal U.S. nonfarm productivity from 1991-1995, and x represents the end of the year with 1991 corresponding
to x=1, and 1992 corresponding to x=2, and so on.
a. Give the function that describes total productivity in year x, if productivity was 115
in 1992.
b. Use your function from part a to find productivity at the end of 1994. In 1994,
productivity actually measured 118.6. How does your value using the function
compare with this?
20. Linear Motion: A particles is moving along a straight line with velocity v t  t 2  2t . Its
bg
bg
bg
bg
bg
distance from the starting point after 3 sec is 8 cm. Find s t , the distance of the particle from the
starting point after t sec.
21. Net Savings: A company has installed new machinery that will produce a savings rate (in
thousands of dollars per year) of S ' x  225  x 2 , where x is the number of years the machinery is
to be used. The rate of additional costs (in thousands of dollars per year) to the company due to
the new machinery is expected to be C ' x  x 2  25x  150 . For how many years should the
company use the new machinery? Find the net savings (in thousands of dollars) over this period.
22. Infection Rate: The rate of infection of a disease (in people per month) is given by the function
100t
I' t  2
, where t is the time in months since the disease broke out. Find the total number of
t 1
infected people over the first four months of the disease.
Integrate/evaluate.
bg
bg
bg
23.
zzcx y  yhdxdy
2
1
3
3
24.
0
ANSWERS
Practice Set A
1. f ' x  10 x 4
bg
zz b2x  3ygdxdy
1
2 y
0
y
bg c hb g
5. f '  x  
4. f ' bg
x  x  3b
3x  2gbg
3  2 xb
3x  2g
2
81914768 Page 10
25.
3
2. f ' x  8 x 2  3 2 x
2
3
zzc
2
4
0
0
bg 2
3. f ' x 
2
3
x
h
x 2 y 2  5x dxdy
9x2  4
3x 3  4 x
c hb gc h
25c
x  1h
x  x e  4x e
8. f ' bg
9. f ' bg
x 
10. e
b2 x  7g
x  2 xe  e  e  3x
x e
 b
x  7g 12. f ' bg
11. f ' bg
x  c
e  3x hc
e  3h 13. f ' bg
e j e j
dy x   5 x ln x
14. f ' bg
x  5c
e  1h 3e
15. f ' bg
x 
16.

e j
dx
x
c h
7. f ' bg
x 
6. f '  x   10 x 2
2
3
5 x 2  1  12 x 2  10 x 2  1 2 x 4 x 3
4 x
x 7
 21
1
2
4
3x
 21
x
1
2
dy 4 x 3  e x
 4
dx
x  ex
bg
3
bg
24.
 23
3x
1
3
bg
32. f ' x 
1x
2
1
2
bg
35. f ' x  3x 2 ln x 
33. f ' x 
x3
4
x
f ' x 
hc3e
9
3x
4
h
3
1
2 2
1
2
x  1 x2
1
bg
31. f ' x   e
12
ce
3x
x
ex
 2
x
bg 1 2x
34. f ' x 
h
c3x  x h5x  2e  5e  b3  2 xgc5xe h
36. f ' bg
x 
c3x  x h
e
3 x 2
2
2x
2
2x
2x
2 2
2
3
4
4
bgc
hc hc hc
4
bg
40. f ' x  5e5 x  3x 2  xe x  e x
c hb2 xg
x 
42. f ' bg
cx  4h
dy 2 x ln x
2x

b
ln x g
 2 ln x  2
44.
dx
x
x
4 x2  4
2
4
4
hc h
38. f ' x  4 x 3  3x 5 e4 x  3 4e4 x  12 x 2  3 e4 x  3
3
4
2
81914768 Page 11
25. f ' x  10 e3 x  4 x
  7  3 x   4  5 x  3   5  5  8 x    5 x  3   8   2  7  3 x  3   5 x  3   5  8 x  
 7  3x 


 5 x  3  5  8 x  
 7  3x 

2
37.
dy
1

dx x ln x
b g
20c
lnb
4 x  5g
4
hbg
x 
27. f ' bg
4x  5
1 c
1  x hb
2 xg
29. f ' bg
x 
 21
bg
e x
ex

2 x 2 ex
22.
bg c
4e 4 x  5 x5 2
dy

dx 2 e 4 x  ln 5x  2
2
1x
2
2
hbgb gb g
cx  3xhb9 x  2g
b g
2
1
2
4
x
10
dx
3x
2
1
x
5
c
ce  xhc3e  1h
cx  1h1  ln x  1  2 x x ln x  x
28. f ' bg
x 
cx  1h
x  e
x 1  e b
x  1g
30. f ' bg
dy

dx
2x
x 2
dy
4e 5 x

 5e5 x ln 4 x  2
dx 4 x  2
21.
2x
x 2  3x 9  2 x  3 9 x  2
19. dy 
2
dy 1

dx x
18.
dy 4 ln x
20.

dx
x
2x  5
23. f ' x  2
x  5x
26.
x
1 e x e x   e x e x
3x
1 e
17.
x 2 7 x
x 4 e x  4 x 3e x
x8
3 x
4
2
5
bg lnc3x
39. f ' x 
e2 x 4 x 3  3
6x  7
2
hc
h
lnc
x  3x  2h
 7 x  2 3x 2  7 x  2
bg x  3x  2  2e
1
43. f ' bg
x 
lnb
ln x g
x
bln xgbg
41. f ' x 
45.
4
2x
dy
2 x 3e 2 x  3x 2 e 2 x
 2e 2 x 
dx
x6
4
b g  ln x bln xg
46. f ' bg
x 
1 b
ln x g
1  ln x
2
1
x
2e2 x  2 x3e2 xx6 3x2e2 x
47.
2
x
2 2
48.
4
(e x e x )2
50. 13 ( 53xx12 )
 23
49.

(3 x 1)53(5 x  2)
(3 x 1)2
Practice Set B
1. 2x 2  C
6. 2 y  C

51.
2 x3 1
x ( x2 1)2

3. 53 t 3  C
7. z 2  3 z  C
8.
52.
3
2
4.
x2  5x  C
12. 53 x3  3x 2  3x  C
14. 3 y 4  2 y3  4 y 2  5 y  C
15.
5
2 x 1
(1 (ln x ) )
2. 4x 2  C
10
3
1
2 (6 x 2 )( x ( x 2 1) 2 )
3
(1 (ln x ) 2 ) 1x  (2ln x )( 1x )(ln x )
2 2
11. 13 t 3  2t 2  5t  C
3
2 x3 1(2 x ( x2 1)(2 x ) ( x2 1)2 )  12 (2 x3 1)
3
2
10 x3
ln(5 x2 3 x ) (5 x2 3 x )


5. 6k  C
x4  C
9. 13 x 3  3 x 2  C
10. 13 t 3  t 2  C
13. z 4  z 3  z 2  6 z  C
3
5
z2  C
16. 54 t 4  C
3
5
19. 6x 2  43 x 2  C
21. 4u 2  4u 2  C
5
7
22. 16t 2  4u 2  C
23.  z 1  C
24. 2x 2  C
25.  12 y 2  2 y 2  C
26. 23 u 2  u 1  C
27. 9t 1  2 ln t  C
28. 4 x 2  4 ln x  C
29. 12 e2t  C
30.  13 e 3 y  C
31. 15e.2 x  C
32. 20e.2 v  C
35. ln t  23 t 3  C
33. 3ln x  8e .5 x  C
36. 4 y 2  32 y 2  C
34. 9 ln x  7.5e.4 x  C
37. 12 e2u  2u 2  C
38. 13 v3  13 e3v  C
39. 13 x3  x 2  x  C
40.
17. 23 u 2  52 u 2  C
20.
2
3
3
1
x 2  2x 2  C
3
41.
6
7
7
5
18. 83 v 2  56 v 2  C
7
2
42.
3
2
5. eb  ea
6.
9. 12 e 2  12
10.
12. 2
13.
14.
17. 9 56
18. 4 12
20. 19.95
21. 148.05
2
3
19. 12
27. 30
25. 17 13
26. 51 16
28. 3 34
Practice Set D
1. 5 5 6
3. 4 12 25
2. 76
4. 4 ½
Practice Set E
1. 14.87
2. 24
3. 4 ½
Practice Set F
1. 54 x5  2 x3  9 x  C
2. 4e x  C
4.
y3  2 y 2  y  C
43. f ( x)  53 x 3
4. eb  1
11.
4
3
5
2
z 3  z2  C
44. f ( x)  2 x3  2 x 2  3x  1
Practice Set C
1. 16
2. 56
3. 154
e2 3
2
5
34
a3
6
4
13
7. 74 2 3
3. 6ln x  C
x3  10 x 2  25 x  C
9. 39.05
Practice Set G
81914768 Page 12
1
5
8. 6
5. 10 2 3
4. 16
8. 114
11. 21
16.
6. 32 2 3
10
1
15. 4
5. 2.79
6.
7. 65 x 3  9 x 3  C
10. 41.74
8. b 4  a 4
29. 5 13
5. 20
7
7. b3  a 3
24. 5
22. 15 34
23. 7 13
30. 8 31. 14 23 32. 12 33.
 74 x 4  C
5
2x2
9
1
1
x 6  32 x 3  C
3
12. 95 ln(2  5t )  C
4
3
13.
1
4 2 B 4 8 B
C
5
6
1. 52 (2 x  3)5  C
4
3
5.  13 ( x  2 x  4)  C
2
9. 2e
14.
ex
2p
3 3 x
3
6.
2 x3  7
C
7. 13 ( z 2  5)  C
C
15. e z  C
16. e
19. .0034
20. 36
.3 g
C
5e
.3
3.
C
3
20
3. 348 76
9. 3ln( x 2  4)  C
Practice Set K
1. 3 13
2.  27
3. 2 152
20
Practice Set L
1. 159 121
2. 5 53
7. 13 (ln x)3  C
y
C
4. 20 23
5. 3 13
1
5
5
C
6. 1
3. 4
3
6.
1
14
2
22. 54
7. 21 56
(2 x  5) 7  C
1
15
( x3  2)5  C
12. 12 12
2
8. 16
8. 20 56
7.
11. 12 e x  C
7. 6 23
C
3
C
6. 39
1
40
ln(3  x)
5. 3.6
8ln(1 3 x )
3
3
2
13. 12 e2t t  C
21. 8
8. 94 (2  x3 ) 4  C
Practice Set M
1. 2 x 2  5x  8
17.
5.
10.
8.
2
4. 4
4. 57 809
 r  2
2
12.  12 e r  C
11. 12 e2 x  C
3
1
4. 2 3x  5  C
3
2
10.
Practice Set J
1. 154
2. 12 23
1
3( x3 5)
2
C
18. 697
Practice Set H
1. 945
2. 6
8.
3.  12 (2m  1) 2  C
2.  ( 416t 1)  C
9. 18
4. 12 23
5. 138
9. 4e 2  4e
10. 22
13. 14.48
10. 6
11. 31 13
6. 12 ln( x 2  4)  C
11. 6 56
3. 3e.01x  5 4. ln x  x 2  7.45 5. x 2  20 x  50
6a. .029 x 4 .601x 3  3.43x 2  3.24 x .26 6b. 56.8% 7a.
.00039 x 4  .0104 x3  .132 x 2  .137 x  2.4
7b. 2.4
8. 13 t 3  t  6 2t 3  2t  4
9. 2t 3  2t  4
10. 16t 2  6400 , 20 secs.
2.
11. 3t 3  4t 2  2t  14
Practice Set N
1
2
x 2  1x  4
12. 10t 2  3et  1
3
2.  13  x 2  2 x  4   C
1.  12  2m  1  C
3
2
cr  2h C 4.  e  C
b8  r g b8  r g C 7a. cx  50h 137919 7b. 7
9b. 10000
9a. Pbg
x   e  10000
bp  1g bp  1g C 6.
8b. no
5 x  eh
4
8a. 6 lnc
tg
 155.3337e
 144.6663
10a. N b
5.
7
1
7
1
6
6
8
5
2
5
2
6. No
9b. 12.77
3. 2 23
7a. 254.4 million
10. 95 ln 2  5t  C
b g
Practice Set Q
2. 7 2 3
1. 4.76
4d. 2885 5a. 10
3a. 8
5b. 833.6
3
2
2
1
3
3
2
64
3
 x2
1
2
5a. 75
8. 33.34%
b r g C
1
r
11. 1/2
4b. 37477 4c. 
7b. 73 million
11.
3
2
10b. 7537
4a. 46341
r2
1
2
1
3
1
2
.3218876 t
Practice Set P
1. 54
2. 1
3.
9a. 14.75 billion
c
2
5b. 25
12.  41 2 B 4  8 B
hC
 21
3b. 147.9
3c. 770.7 4a. 39
4b. 3369 4c. 484
3
3
6. 12932 7. 27 8. 1 x 2  12 2  C
9. 13 1 ln x  C
3
c
b g
h
Practice Set R
1.
2
3
x 2  9x 3  C
81914768 Page 13
3
1
2.
2
x2
C
3.  23 e 2 x  C
4.
1
6
e3x  C
2
5.
3
2
c h
c h C
ln x 2  1  C
9. 14.33
10.
5
8
6.  91 x 3  5
e 24  85 e 4
bg b g
bg
3
11. 138
7.
12.
64
3
1
5
cx  5xh C
5
2
13.
1
6
bg
8.  121 e 3 x  C
4
14. 54
3
17. 26.3 18. 36
.
19a. f x  109e.0198 x  16
16. C x  2 x  1 2  145
21. 2.5; 99000 22. 141.66 23. 34 78
24. 3
20. s t  13 t 3  t 2  8
81914768 Page 14
15. 32
19b. 119.58; 1
25. 136 89