Calculus

# SOLUTION: CC Calculus Worksheet – Studypool

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

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