Question 1

Write the formula for Newton's method and use the given initial approximation to compute the approximations   and   . Round to six decimal places.
-f(x) =   - 30;   = 5

Accepted Answer

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

Question 2

Solve the problem. 
-Given the velocity and initial position of a body moving along a coordinate line at time t, find the body's position at time t. v = cos   t, s(0) = 1

Accepted Answer

A)  s =   sin   t 
B)  s = 2$\pi$ sin   t 
C)  s = sin t 
D)  s =   sin   t + $\pi$ 
A)  s =   sin   t 
B)  s = 2$\pi$ sin   t 
C)  s = sin t 
D)  s =   sin   t + $\pi$

Question 3

Choose the one alternative that best completes the statement or answers the question.
-The graph below shows the first derivative of a function   . Select a possible graph f that passes through the point P.

Accepted Answer

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

Question 4

Find the largest open interval where the function is changing as requested.
-Increasing f(x) =   x2 -   x

Accepted Answer

A)  (-1, 1) 
B)  (-$\infty$, -1) 
C)  (-$\infty$, $\infty$) 
D)  (1, $\infty$) 
A)  (-1, 1) 
B)  (-$\infty$, -1) 
C)  (-$\infty$, $\infty$) 
D)  (1, $\infty$)

Question 5

Find the absolute extreme values of the function on the interval.
-f(x) = csc x, -   $\le$x $\le$

Accepted Answer

A)  absolute maximum is 1 at x =  $\pi$; absolute minimum is -1 at x =  $\pi$ 
B)  absolute maximum does not exist; absolute minimum does not exist 
C)  absolute maximum is 0 at x = - $\pi$; absolute minimum is -1 at x =  $\pi$ 
D)  absolute maximum is -1 at x = $\pi$; absolute minimum is 1 at x = 0 
A)  absolute maximum is 1 at x =  $\pi$; absolute minimum is -1 at x =  $\pi$ 
B)  absolute maximum does not exist; absolute minimum does not exist 
C)  absolute maximum is 0 at x = - $\pi$; absolute minimum is -1 at x =  $\pi$ 
D)  absolute maximum is -1 at x = $\pi$; absolute minimum is 1 at x = 0

Question 6

Find the value or values of c that satisfy the equation   =   (c) in the conclusion of the Mean Value Theorem for the function and interval.
-f(x) = x +   ,

Accepted Answer

A)  0, 2   
B)  -2   , 2   
C)  3, 4 
D)  2   
A)  0, 2   
B)  -2   , 2   
C)  3, 4 
D)  2

Question 7

Find the extreme values of the function and where they occur.
-y = x2 + 2x - 3

Accepted Answer

A)  Absolute minimum is 1 at x = 4. 
B)  Absolute minimum is -4 at x = -1. 
C)  Absolute minimum is -1 at x = 4. 
D)  Absolute minimum is 1 at x = -4. 
A)  Absolute minimum is 1 at x = 4. 
B)  Absolute minimum is -4 at x = -1. 
C)  Absolute minimum is -1 at x = 4. 
D)  Absolute minimum is 1 at x = -4.

Question 8

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

Accepted Answer

A)  8 
B)  2 
C)  -2 
D)  14 
A)  8 
B)  2 
C)  -2 
D)  14

Question 9

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

Accepted Answer

A)  1 
B)  0 
C)  4/3 
D)  1/6 
A)  1 
B)  0 
C)  4/3 
D)  1/6

Question 10

Sketch the graph and show all local extrema and inflection points.
-y =   - 6   - 7x

Accepted Answer

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

Question 11

Determine all critical points for the function.
-f(x) =

Accepted Answer

A)  x = -12 and x = 0 
B)  x = 2 
C)  x = -2 
D)  x = 0 and x = 2 
A)  x = -12 and x = 0 
B)  x = 2 
C)  x = -2 
D)  x = 0 and x = 2

Question 12

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

Accepted Answer

A)  9/8 
B)  1 
C)  9 
D)  $\infty$ 
A)  9/8 
B)  1 
C)  9 
D)  $\infty$

Question 13

Find the absolute extreme values of the function on the interval.
-F(x) = -   , 0.5 $\le$x $\le$ 2

Accepted Answer

A)  absolute maximum is 1/2 at x = 1/ 2; absolute minimum is -8 at x = 2 
B)  absolute maximum is - 1/2 at x = 2 ; absolute minimum is -8 at x = 1/2 
C)  absolute maximum is - 1/2 at x = 1/ 2; absolute minimum is -8 at x = - 2 
D)  absolute maximum is at x = -1/2 at x = 2 ; absolute minimum is -8 at x = -1/2 
A)  absolute maximum is 1/2 at x = 1/ 2; absolute minimum is -8 at x = 2 
B)  absolute maximum is - 1/2 at x = 2 ; absolute minimum is -8 at x = 1/2 
C)  absolute maximum is - 1/2 at x = 1/ 2; absolute minimum is -8 at x = - 2 
D)  absolute maximum is at x = -1/2 at x = 2 ; absolute minimum is -8 at x = -1/2

Question 14

Find the absolute extreme values of the function on the interval.
-f(x) = 7   , -27 $\le$ x $\le$8

Accepted Answer

A)  absolute maximum is 1792 at x = 8 ; absolute minimum is 0 at x = 0 
B)  absolute maximum is 6561 at x = -27 ; absolute minimum is 0 at x = 0 
C)  absolute maximum is 45,927 at x = -27 ; absolute minimum is 0 at x = 0 
D)  absolute maximum is 45,927 at x = -27 ; absolute minimum is 1792 at x = 8 
A)  absolute maximum is 1792 at x = 8 ; absolute minimum is 0 at x = 0 
B)  absolute maximum is 6561 at x = -27 ; absolute minimum is 0 at x = 0 
C)  absolute maximum is 45,927 at x = -27 ; absolute minimum is 0 at x = 0 
D)  absolute maximum is 45,927 at x = -27 ; absolute minimum is 1792 at x = 8

Question 15

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

Accepted Answer

A) True 
 B)False

Question 16

Choose the one alternative that best completes the statement or answers the question. 
-A window is in the form of a rectangle surmounted by a semicircle. The rectangle is of clear glass, whereas the semicircle is of tinted glass that transmits only one-third as much light per unit area as clear glass does. The total perimeter is fixed. Find the proportions of the window that will admit the most light. Neglect the thickness of the frame.

Accepted Answer

A)    = 12/ 6 +  $\pi$ 
B)    = 3/ 6 + 2 $\pi$ 
C)    = 12/ 6+ 2 $\pi$ 
D)    = 12/3+2 $\pi$ 
A)    = 12/ 6 +  $\pi$ 
B)    = 3/ 6 + 2 $\pi$ 
C)    = 12/ 6+ 2 $\pi$ 
D)    = 12/3+2 $\pi$

Question 17

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

Accepted Answer

A)  0 
B)  9 
C)  3 
D)  $\infty$ 
A)  0 
B)  9 
C)  3 
D)  $\infty$

Question 18

Use Newton's method to approximate all the intersection points of the pair of curves. Some preliminary graphing or analysis may help in choosing good initial approximations. Round to six decimal places.
-y =   -   and y =   - 3

Accepted Answer

A)  x $\approx$ -1.030885, 1.549296, 2.530979 
B)  x $\approx$-0.880495, 1.599796, 2.732089 
C)  x $\approx$ -0.626885, 1.346186, 2.332089 
D)  x $\approx$ -0.879385, 1.347296, 2.532089 
A)  x $\approx$ -1.030885, 1.549296, 2.530979 
B)  x $\approx$-0.880495, 1.599796, 2.732089 
C)  x $\approx$ -0.626885, 1.346186, 2.332089 
D)  x $\approx$ -0.879385, 1.347296, 2.532089

Question 19

Write the formula for Newton's method and use the given initial approximation to compute the approximations   and   . Round to six decimal places.
-f(x) =   -   ;   = ln 2

Accepted Answer

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

Question 20

Find an antiderivative of the given function. 
-  -

Accepted Answer

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

Write the formula for Newton's method and use the given initial approximation to compute the approximations and . Round to six decimal places. -f(x) = - 30; = 5

Solve the problem. -Given the velocity and initial position of a body moving along a coordinate line at time t, find the body's position at time t. v = cos t, s(0) = 1

Choose the one alternative that best completes the statement or answers the question. -The graph below shows the first derivative of a function . Select a possible graph f that passes through the point P.

Find the largest open interval where the function is changing as requested. -Increasing f(x) = x² - x

Find the absolute extreme values of the function on the interval. -f(x) = csc x, - $Find the absolute extreme values of the function on the interval. -f(x) = csc x, - \le x \le$ $\le$ x $\le$ $Find the absolute extreme values of the function on the interval. -f(x) = csc x, - \le x \le$

Find the value or values of c that satisfy the equation = (c) in the conclusion of the Mean Value Theorem for the function and interval. -f(x) = x + ,

Find the extreme values of the function and where they occur. -y = x² + 2x - 3

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

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

Sketch the graph and show all local extrema and inflection points. -y = - 6 - 7x

Determine all critical points for the function. -f(x) =

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

Find the absolute extreme values of the function on the interval. -F(x) = - $Find the absolute extreme values of the function on the interval. -F(x) = - , 0.5 \le x \le 2$ , 0.5 $\le$ x $\le$ 2

Find the absolute extreme values of the function on the interval. -f(x) = 7 $Find the absolute extreme values of the function on the interval. -f(x) = 7 , -27 \le x \le 8$ , -27 $\le$ x $\le$ 8

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

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

Use Newton's method to approximate all the intersection points of the pair of curves. Some preliminary graphing or analysis may help in choosing good initial approximations. Round to six decimal places. -y = - and y = - 3

Write the formula for Newton's method and use the given initial approximation to compute the approximations and . Round to six decimal places. -f(x) = - ; = ln 2

Find an antiderivative of the given function. - -

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

Exam 4: Applications of the Derivative

Write the formula for Newton's method and use the given initial approximation to compute the approximations and . Round to six decimal places. -f(x) = - 30; = 5

Solve the problem. -Given the velocity and initial position of a body moving along a coordinate line at time t, find the body's position at time t. v = cos t, s(0) = 1

Choose the one alternative that best completes the statement or answers the question. -The graph below shows the first derivative of a function . Select a possible graph f that passes through the point P.

Find the largest open interval where the function is changing as requested. -Increasing f(x) = x2 - x

Find the absolute extreme values of the function on the interval. -f(x) = csc x, - ≤\le≤ x ≤\le≤

Find the value or values of c that satisfy the equation = (c) in the conclusion of the Mean Value Theorem for the function and interval. -f(x) = x + ,

Find the extreme values of the function and where they occur. -y = x2 + 2x - 3

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

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

Sketch the graph and show all local extrema and inflection points. -y = - 6 - 7x

Determine all critical points for the function. -f(x) =

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

Find the absolute extreme values of the function on the interval. -F(x) = - , 0.5 ≤\le≤ x ≤\le≤ 2

Find the absolute extreme values of the function on the interval. -f(x) = 7 , -27 ≤\le≤ x ≤\le≤ 8

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

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

Use Newton's method to approximate all the intersection points of the pair of curves. Some preliminary graphing or analysis may help in choosing good initial approximations. Round to six decimal places. -y = - and y = - 3

Write the formula for Newton's method and use the given initial approximation to compute the approximations and . Round to six decimal places. -f(x) = - ; = ln 2

Find an antiderivative of the given function. - -

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 largest open interval where the function is changing as requested. -Increasing f(x) = x² - x

Find the absolute extreme values of the function on the interval. -f(x) = csc x, - $Find the absolute extreme values of the function on the interval. -f(x) = csc x, - \le x \le$ $\le$ x $\le$ $Find the absolute extreme values of the function on the interval. -f(x) = csc x, - \le x \le$

Find the extreme values of the function and where they occur. -y = x² + 2x - 3

Find the absolute extreme values of the function on the interval. -F(x) = - $Find the absolute extreme values of the function on the interval. -F(x) = - , 0.5 \le x \le 2$ , 0.5 $\le$ x $\le$ 2

Find the absolute extreme values of the function on the interval. -f(x) = 7 $Find the absolute extreme values of the function on the interval. -f(x) = 7 , -27 \le x \le 8$ , -27 $\le$ x $\le$ 8