Math 125 HW_2A
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WebAssign
Math 125 HW_2A (Homework)
Current Score : – / 70
Donald Marshall
Math 125 Spring 2014, section A, Spring 2014
Instructor: Donald Marshall
Due : Friday, April 11 2014 11:00 PM PDT
4/11/2014 12:43 PM
Math 125 HW_2A
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1. –/8 points
SCalcET7 5.3.003.
Let g(x) =
x
f(t) dt, where f is the function whose graph is shown.
(a) Evaluate g(0), g(5), g(10), g(15), and g(30).
g(0) =
g(5) =
g(10) =
g(15) =
g(30) =
(b) On what interval is g increasing? (Enter your answer using interval notation.)
(c) Where does g have a maximum value?
x=
(d) Sketch a rough graph of g.
4/11/2014 12:43 PM
Math 125 HW_2A
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2. –/5 points
SCalcET7 5.3.009.
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.
s
g(s) =
8 3
(t − t ) dt
g'(s) =
3. –/5 points
SCalcET7 5.3.015.
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.
tan x
y=
t dt
5t +
y' =
4. –/5 points
SCalcET7 5.3.017.
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.
2
y=
u
− 3x
3
2
1+u
du
y' =
5. –/5 points
SCalcET7 5.3.021.
Evaluate the integral.
4
2
(7 − 2t + 3t ) dt
6. –/5 points
SCalcET7 5.3.035.
Evaluate the integral.
2
3
7
v + 6v
2
v
dv
4/11/2014 12:43 PM
Math 125 HW_2A
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7. –/5 points
SCalcET7 5.3.041.
Evaluate the integral.
3
2
u+2
e
du
8. –/5 points
SCalcET7 5.3.052.
Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area.
2
y = sec x,
0 ≤ x ≤ π/4
9. –/5 points
SCalcET7 5.3.055.
Find the derivative of the function.
g(x) =
5x
x
2
u −3
2
u +3
du
Hint:
5x
x
f(u) du =
0
x
f(u) du +
5x
f(u) du
g'(x) =
10.–/5 points
If f(2) = 12, f ' is continuous, and
SCalcET7 5.3.063.
5
f '(x) dx = 20, what is the value of f(5)?
f(5) =
4/11/2014 12:43 PM
Math 125 HW_2A
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11.–/12 points
SCalcET7 5.3.067.
Let g(x) =
x
f(t) dt, where f is the function whose graph is shown.
(a) At what values of x do the local maximum and minimum values of g occur?
x
min
=
(smaller x-value)
min
=
(larger x-value)
x
max
=
(smaller x-value)
x
=
(larger x-value)
x
max
(b) Where does g attain its absolute maximum value?
x=
(c) On what interval is g concave downward? (Enter your answer using interval notation.)
(d) Sketch the graph of g.
4/11/2014 12:43 PM
Math 125 HW_2A
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12.–/5 points
SCalcET7 5.3.078.
The area labeled B is six times the area labeled A. Express b in terms of a.
b=
4/11/2014 12:43 PM