SOLUTION: CC Calculus Worksheet – Studypool

Test Chap 4-5
M121
Form A
Exponential/Log Derivatives and Integration
NAME ________________________________
Part 1 Derivatives
1. Find
f ‘ ( x) :
DATE
_________________
with Types power, exp, and ln
Circle your answers
f ( x) = ln( 1 − 2 x )
3
Type _______
2.
Find
f ‘ ( x) :
f ( x) = 3e −3 x
3.
Find dy/dx:
f ( x) = 4 x ln( x)
4.
d
[3 ln( 1 + e 2 x )]
dx
Type _______
Part 2 Integration
_______
U=
U’ = _______
_______
U’ = _______
{Hint: uses product rule}
Type _______
5. Use the Quotient rule to find
U=
U=
f ‘ ( x ) for
_______
f ( x) =
U’ = _______
2x 2
e2x
using types power, exp, and ln
Circle your answers
please
6.
 (4 x
3
− 2 x + 1)dx
Type _______
U=
_______
U’ = _______
(
7.
1
8.
x
3
x+
3
+ e 3 x )dx
x
1
x 2 dx
+1
Type _______
9.
 (x
3
+ 2) 8 2 x 2 dx
1
10. Evaluate:
____
_____
U=
_______
U’ = _______
{rounded to 3 decimal places}
3
0
Types ____
 6e
Type _______
( 2 t −1)
dt
U=
_______
U=
U’ = _______
_______
U’ = _______
{rounded to 1 decimal place}
0
`Type _______
U=
_______
U’ = _______
11.
 (x
12.
x
6x
dx
+ 1) 4
2
2 x 2 + 1dx
Type _______
U=
_______
U’ = _______
Type _______
U=
_______
U’ = _______
y = x2 −1
and
13. Shade and find the area of the region between
x = 0 to x = 2.
y = 2x 2 + 1
from
14.
A company’s marginal cost is given by:
1
C ‘ ( x) =
2x + 1
=
rewrite =
__________ Fixed costs are $50 (That is:
C(0) = $50)
a. Find the cost function C(x)in radical form.
Type _______
b.
15.
f(x) =
U=
_______
U’ = _______
Find the cost of the first 10 items (to the nearest cent)
Find f(x)
if
f ‘ ‘ ( x) = 4 x + 1
and f’(0) = 2
________________________________________
and f(0) = 3
Bonus: Sketch and Shade the area between y = x − 1 and y = − x + 1 from x = 0
to x = 2. The graphs intersect at x = 1 so there will be two integrals and two
regions to shade.
2
Answer
________
square units

Purchase answer to see full
attachment