Question 1

Find the most general antiderivative.      
-  d$\theta$

Accepted Answer

A)  cot $\theta$+ C 
B)  $\theta$ + tan $\theta$ + C 
C)  -cot $\theta$+ C 
D)    $\theta$ + C 
A)  cot $\theta$+ C 
B)  $\theta$ + tan $\theta$ + C 
C)  -cot $\theta$+ C 
D)    $\theta$ + C

Question 2

Sketch the graph and show all local extrema and inflection points.
-y = x

Accepted Answer

A)  
  
B)  
  
C)  
  
D)  
  
A)  
  
B)  
  
C)  
  
D)

Question 3

Find the linearization L(x) of f(x) at x = a.
-f(x) =   , a = 0

Accepted Answer

A)  L(x) = 1/4 x 
B)  L(x) = -1/4 x 
C)  L(x) = - 1/2 x 
D)  L(x) = 1/2 x 
A)  L(x) = 1/4 x 
B)  L(x) = -1/4 x 
C)  L(x) = - 1/2 x 
D)  L(x) = 1/2 x

Question 4

Use differentiation to determine whether the integral formula is correct.
-

Accepted Answer

A) True 
 B)False

Question 5

Express the relationship between a small change in x and the corresponding change in y in the form   . 
-y = x

Accepted Answer

A)  
  
B)  
  
C) 
   
D)  
  
A)  
  
B)  
  
C) 
   
D)

Question 6

Determine the indefinite integral. Check your work by differentiation.
-  dx

Accepted Answer

A)  
  
B)  
  
C)  
  
D)  
  
A)  
  
B)  
  
C)  
  
D)

Question 7

Sketch the graph and show all local extrema and inflection points.
-y = -   + 4   - 2

Accepted Answer

A)    
B)    
C)    
D)  
  
A)    
B)    
C)    
D)

Question 8

Find the largest open interval where the function is changing as requested.
-Decreasing f(x) =

Accepted Answer

A)  (-$\infty$, -8) 
B)  (8, $\infty$) 
C)  (-$\infty$, 8) 
D)  (-8, $\infty$) 
A)  (-$\infty$, -8) 
B)  (8, $\infty$) 
C)  (-$\infty$, 8) 
D)  (-8, $\infty$)

Question 9

Express the relationship between a small change in x and the corresponding change in y in the form   . 
-y = 2 cot

Accepted Answer

A)  
  
B)  
  
C)  
  
D)  
  
A)  
  
B)  
  
C)  
  
D)

Question 10

Find all the roots of the function. Use preliminary analysis and graphing to determine good initial approximations. Round to six decimal places.
-f(x) = cos 4x -   + 5

Accepted Answer

A)  x $\approx$ -4.859572, 1.859572 
B)  x $\approx$ -3.470572, 3.248572 
C)  x $\approx$ -3.248572, 3.470572 
D)  x $\approx$ -3.359572, 3.359572 
A)  x $\approx$ -4.859572, 1.859572 
B)  x $\approx$ -3.470572, 3.248572 
C)  x $\approx$ -3.248572, 3.470572 
D)  x $\approx$ -3.359572, 3.359572

Question 11

Determine whether the function satisfies the hypotheses of the Mean Value Theorem for the given interval.
-g(x) =   ,

Accepted Answer

A) True 
 B)False

Question 12

Find the absolute extreme values of the function on the interval.
-F(x) =   , -1 $\le$ x $\le$27

Accepted Answer

A)  absolute maximum is 3 at x = 27; absolute minimum is 0 at x =0 
B)  absolute maximum is 3 at x = 27; absolute minimum is -3 at x = -27 
C)  absolute maximum is 0 at x = 0; absolute minimum is 3 at x = 27 
D)  absolute maximum is 3 at x = -27; absolute minimum is 0 at x =0 
A)  absolute maximum is 3 at x = 27; absolute minimum is 0 at x =0 
B)  absolute maximum is 3 at x = 27; absolute minimum is -3 at x = -27 
C)  absolute maximum is 0 at x = 0; absolute minimum is 3 at x = 27 
D)  absolute maximum is 3 at x = -27; absolute minimum is 0 at x =0

Question 13

Find an antiderivative of the given function. 
-2

Accepted Answer

A)  
  
B)  
  
C)  
  
D)  
  
A)  
  
B)  
  
C)  
  
D)

Question 14

Solve the problem. 
-At about what velocity do you enter the water is you jump from a 15 meter cliff? (Use g = 9.8 m/   .)

Accepted Answer

A)  2 m/sec 
B)  -8.5 m/sec 
C)  -17 m/sec 
D)  17 m/sec 
A)  2 m/sec 
B)  -8.5 m/sec 
C)  -17 m/sec 
D)  17 m/sec

Question 15

Solve the problem.
-A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of   What dimensions yield the minimum surface area? Round to the nearest tenth, if necessary.

Accepted Answer

A)  5.1 ft × 5.1 ft × 1.7 ft 
B)  3.5 ft × 3.5 ft × 3.5 ft 
C)  4.5 ft × 4.5 ft × 2.2 ft 
D)  9.4 ft × 9.4 ft × 0.5 ft 
A)  5.1 ft × 5.1 ft × 1.7 ft 
B)  3.5 ft × 3.5 ft × 3.5 ft 
C)  4.5 ft × 4.5 ft × 2.2 ft 
D)  9.4 ft × 9.4 ft × 0.5 ft

Question 16

Find the absolute extreme values of the function on the interval.
-h(x) =   x + 5, -2 $\le$ x $\le$ 3

Accepted Answer

A)  absolute maximum is - 7/2 at x = -2; absolute minimum is 4 at x = 3 
B)  absolute maximum is 13/2 at x = 3; absolute minimum is 4 at x = -2 
C)  absolute maximum is - 7/2 at x = -3; absolute minimum is -3 at x = 2 
D)  absolute maximum is - 7/2 at x = 3; absolute minimum is 4 at x = -2 
A)  absolute maximum is - 7/2 at x = -2; absolute minimum is 4 at x = 3 
B)  absolute maximum is 13/2 at x = 3; absolute minimum is 4 at x = -2 
C)  absolute maximum is - 7/2 at x = -3; absolute minimum is -3 at x = 2 
D)  absolute maximum is - 7/2 at x = 3; absolute minimum is 4 at x = -2

Question 17

Find an antiderivative of the given function. 
--

Accepted Answer

A)  
  
B)  
  
C)  
  
D)  
  
A)  
  
B)  
  
C)  
  
D)

Question 18

L'Hopital's rule does not help with the given limit. Find the limit some other way.
-

Accepted Answer

A)  -1 
B)  0 
C)  $\infty$ 
D)  1 
A)  -1 
B)  0 
C)  $\infty$ 
D)  1

Question 19

Use l'Hopital's Rule to evaluate the limit.
-

Accepted Answer

A)    
B)  -   
C)    
D)  -   
A)    
B)  -   
C)    
D)  -

Question 20

Find the extreme values of the function and where they occur.
-y =

Accepted Answer

A)  Absolute maximum value is 0 at x = 0. 
B)  Absolute minimum value is 0 at x = 1. Absolute maximum value is 0 at x = -1. 
C)  Absolute minimum value is - 1 at x = -1. Absolute maximum value is 1at x = 1. 
D)  Absolute minimum value is 0 at x = 0. 
A)  Absolute maximum value is 0 at x = 0. 
B)  Absolute minimum value is 0 at x = 1. Absolute maximum value is 0 at x = -1. 
C)  Absolute minimum value is - 1 at x = -1. Absolute maximum value is 1at x = 1. 
D)  Absolute minimum value is 0 at x = 0.

Find the most general antiderivative. - $Find the most general antiderivative. - d \theta$ d $\theta$

Sketch the graph and show all local extrema and inflection points. -y = x

Find the linearization L(x) of f(x) at x = a. -f(x) = , a = 0

Use differentiation to determine whether the integral formula is correct. -

Express the relationship between a small change in x and the corresponding change in y in the form . -y = x

Determine the indefinite integral. Check your work by differentiation. - dx

Sketch the graph and show all local extrema and inflection points. -y = - + 4 - 2

Find the largest open interval where the function is changing as requested. -Decreasing f(x) =

Express the relationship between a small change in x and the corresponding change in y in the form . -y = 2 cot

Find all the roots of the function. Use preliminary analysis and graphing to determine good initial approximations. Round to six decimal places. -f(x) = cos 4x - + 5

Determine whether the function satisfies the hypotheses of the Mean Value Theorem for the given interval. -g(x) = ,

Find the absolute extreme values of the function on the interval. -F(x) = $Find the absolute extreme values of the function on the interval. -F(x) = , -1 \le x \le 27$ , -1 $\le$ x $\le$ 27

Find an antiderivative of the given function. -2

Solve the problem. -At about what velocity do you enter the water is you jump from a 15 meter cliff? (Use g = 9.8 m/ .)

Solve the problem. -A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of What dimensions yield the minimum surface area? Round to the nearest tenth, if necessary.

Find the absolute extreme values of the function on the interval. -h(x) = $Find the absolute extreme values of the function on the interval. -h(x) = x + 5, -2 \le x \le 3$ x + 5, -2 $\le$ x $\le$ 3

Find an antiderivative of the given function. --

L'Hopital's rule does not help with the given limit. Find the limit some other way. -

Use l'Hopital's Rule to evaluate the limit. -

Find the extreme values of the function and where they occur. -y =

Functions

Limits

Derivatives

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

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Exam 4: Applications of the Derivative

Find the most general antiderivative. - d θ\thetaθ

Sketch the graph and show all local extrema and inflection points. -y = x

Find the linearization L(x) of f(x) at x = a. -f(x) = , a = 0

Use differentiation to determine whether the integral formula is correct. -

Express the relationship between a small change in x and the corresponding change in y in the form . -y = x

Determine the indefinite integral. Check your work by differentiation. - dx

Sketch the graph and show all local extrema and inflection points. -y = - + 4 - 2

Find the largest open interval where the function is changing as requested. -Decreasing f(x) =

Express the relationship between a small change in x and the corresponding change in y in the form . -y = 2 cot

Find all the roots of the function. Use preliminary analysis and graphing to determine good initial approximations. Round to six decimal places. -f(x) = cos 4x - + 5

Determine whether the function satisfies the hypotheses of the Mean Value Theorem for the given interval. -g(x) = ,

Find the absolute extreme values of the function on the interval. -F(x) = , -1 ≤\le≤ x ≤\le≤ 27

Find an antiderivative of the given function. -2

Solve the problem. -At about what velocity do you enter the water is you jump from a 15 meter cliff? (Use g = 9.8 m/ .)

Solve the problem. -A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of What dimensions yield the minimum surface area? Round to the nearest tenth, if necessary.

Find the absolute extreme values of the function on the interval. -h(x) = x + 5, -2 ≤\le≤ x ≤\le≤ 3

Find an antiderivative of the given function. --

L'Hopital's rule does not help with the given limit. Find the limit some other way. -

Use l'Hopital's Rule to evaluate the limit. -

Find the extreme values of the function and where they occur. -y =

Functions

Limits

Derivatives

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Find the most general antiderivative. - $Find the most general antiderivative. - d \theta$ d $\theta$

Find the absolute extreme values of the function on the interval. -F(x) = $Find the absolute extreme values of the function on the interval. -F(x) = , -1 \le x \le 27$ , -1 $\le$ x $\le$ 27

Find the absolute extreme values of the function on the interval. -h(x) = $Find the absolute extreme values of the function on the interval. -h(x) = x + 5, -2 \le x \le 3$ x + 5, -2 $\le$ x $\le$ 3