Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Use the Product Rule to differentiate  .
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2.
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Find the x-values (if any) at which the function  is not continuous. Which of the discontinuities are removable? a. | discontinuous everywhere | b. | 3 and - ,
removable | c. | continuous everywhere | d. | 0, removable | e. | 3 and - , not removable |
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3.
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Let  Determine the following limit. (Hint:
Use the graph to calculate the limit.)   a. | 16 | b. | 1 | c. | 5 | d. | 4 | e. | does not
exist. |
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4.
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The graph of the function f is given
below. Select the graph of  . 
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5.
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Find the second derivative of the function
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6.
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Find the limit (if it exists). 
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7.
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A ladder  feet long is leaning against the wall of a
house (see figure). The base of the ladder is pulled away from the wall at a rate of 
feet per second. How fast is the top of the ladder moving down the wall when its base is  feet from the wall? Round your answer to two decimal places.
a. |  ft/sec | b. | 
ft/sec | c. |  ft/sec | d. | 
ft/sec | e. |  ft/sec |
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8.
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Determine the open intervals on which the graph of  is concave
downward or concave upward.
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9.
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Determine the following limit. (Hint: Use the graph to calculate the
limit.) 
a. | 5 | b. | 6 | c. | 1 | d. | 7 | e. | does not
exist |
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10.
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Find the derivative of the following function using the limiting
process.
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11.
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Use the rules of differentiation to find the derivative of the function  .
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12.
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Find the slope of the graph of the function at the given value .  at 
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13.
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Find all critical numbers of the function  . a. | critical numbers:  | b. | critical numbers:
 | c. | critical numbers:
 | d. | critical numbers:
 | e. | no critical
numbers |
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14.
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Complete the table and use the result to estimate the limit.  x | –6.1 | –6.01 | –6.001 | –5.999 | –5.99 | –5.9 | | | | | | | | | | | | | | |
a. | 0.303571 | b. | –0.446429 | c. | –0.071429 | d. | 0.553571 | e. | 0.428571 |
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15.
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Find the sum given below. 
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16.
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Find the limit. 
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17.
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Determine the following limit. (Hint: Use the graph to calculate the
limit.)   a. | –2 | b. | 2 | c. | 0 | d. | –4 | e. | does not
exist |
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18.
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The graph of f is shown below. For which value of x is  zero? 
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19.
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Evaluate the definite integral of the algebraic function.  Use a graphing utility to verify your results.
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20.
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Locate the absolute extrema of the function  on the
closed interval  .
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21.
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Find the indefinite integral and check the result by
differentiation. 
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22.
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Find the equation of the tangent line T to the graph of 
at the given point 
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23.
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Find the derivative of the function  .
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24.
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Find two positive numbers such that the sum of the first and twice the second is
72 and whose product is a maximum.
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25.
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Find the limit L.  a. | L = –4 | b. | L = 12 | c. | L =
6 | d. | L = 2 | e. | none of the
above |
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26.
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The graph of a function f is is shown below.  Sketch the graph of the derivative  .
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27.
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Find the derivative of the function  .
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28.
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Find the derivative of the following function  using the
limiting process.
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29.
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Find the slope of the graph of the function at the given value.  when 
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30.
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Find the derivative of the function. 
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31.
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Use the summation formulas to rewrite the expression  without the
summation notation.
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32.
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Discuss the continuity of the function  . 
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33.
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The height of an object t seconds after it is dropped from a height of
700 meters is  Find the average velocity of the object
during the first 11 seconds. a. | –53.90 m/sec | b. | 53.90 m/sec | c. | 121
m/sec | d. | –121.00 m/sec | e. | –13.00
m/sec |
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34.
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Use the graph to determine the following limits, and discuss the continuity of
the function at  . (i)  (ii)  (iii)  
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35.
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Assume that x and y are both differentiable functions of t
. Find  for the equation  .
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36.
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Find  by implicit differentiation. 
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37.
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Use the Trapezoid Rule to approximate the value of the definite integral  wth  . Round your answer to four decimal
places.
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38.
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Find the derivative of the function  .
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39.
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Find the limit. 
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40.
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Find the limit.  a. | –7 | b. |  | c. | –5 | d. |  | e. | 5 |
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41.
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Evaluate the definite integral of the function.  Use a graphing utility to verify your results.
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42.
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Determine whether Rolle's Theorem can be applied to 
on the closed interval  If Rolle's Theorem can be applied, find
all values of c in the open interval  such that  a. | Rolle's Theorem applies; c = 6, c = 8 | b. | Rolle's Theorem
applies; c = 12 | c. | Rolle's Theorem applies; c = 12,
c = 6 | d. | Rolle's Theorem applies; c = 8 | e. | Rolle's Theorem
does not apply |
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43.
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Use the graph as shown to determine the following limits, and discuss the
continuity of the function at  . (i)  (ii)  (iii)  
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44.
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Evaluate the following definite integral by the limit definition. 
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45.
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a. | Graph 1 | b. | Graph 4 | c. | Graph
2 | d. | Graph 3 | e. | none of the
above |
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46.
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Find the indefinite integral  .
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47.
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The graph of f is shown in the figure. Sketch a graph of the derivative
of f.
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48.
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Evaluate the following definite integral by the limit definition. 
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49.
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Find the limit. 
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50.
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Use the graph as shown to determine the following limits, and discuss the
continuity of the function at  . (i)  (ii)  (iii)   a. |  | b. | 3 , 3 , 3 ,  | c. |  | d. |  | e. | 3 , 3 , 3 ,  |
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51.
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Find the limit. 
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52.
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Find the general solution of the differential equation below and check the
result by differentiation. 
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53.
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Find the general solution of the differential equation below and check the
result by differentiation. 
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54.
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Use the rules of differentiation to find the derivative of the function  .
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55.
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Find the slope 
of the line tangent to the graph of the function  at the point  .
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56.
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All edges of a cube are expanding at a rate of  centimeters
per second. How fast is the volume changing when each edge is 
centimeters?
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57.
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Find the indefinite integral  . a. |  | b. |  | c. |  | d. |  | e. | none of the above |
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58.
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The graph of the function  is given below. Which of
the following definite integrals yields the area of the shaded region? 
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59.
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Suppose the position function for a free-falling object on a certain planet is
given by  . A silver coin is dropped from the top of a
building that is 1380 feet tall. Find the instantaneous velocity of the coin when  . a. | –65 ft/sec | b. | –195 ft/sec | c. | –34
ft/sec | d. | –130 ft/sec | e. | –21
ft/sec |
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60.
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Use Simpson's Rule to approximate the value of the definite integral  with  . Round your answer to four decimal
places.
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61.
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Identify the open intervals where the function  is
increasing or decreasing.
a. |  | b. | increasing on  | c. | decreasing on  | d. | decreasing on  ; increasing on  | e. |  |
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62.
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Use the Product Rule to differentiate. 
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63.
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Find the derivative of the function  .
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64.
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Find the indefinite integral  .
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65.
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Find the indefinite integral  .
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66.
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Find the limit. 
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67.
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Find all relative extrema of the function  . Use the
Second Derivative Test where applicable. a. | no relative max or min | b. | relative max: (1, 5); no relative
min | c. | relative max: (1, 5); relative min: (0, 4) | d. | relative min: (0,
4); no relative max | e. | relative max: (0, 4); no relative
min |
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68.
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Find the indefinite integral  .
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69.
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Find the derivative of the function  .
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70.
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Evaluate the definite integral  . Use a graphing utility to
verify your results.
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71.
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Find all the vertical asymptotes (if any) of the graph of the function  a. |  | b. |  | c. |  | d. |  | e. | no vertical asymptotes |
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72.
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The graph of f is shown. Graph f, f' and
f'' on the same set of coordinate axes.
 a. |  | d. |  | b. |  | e. | none of the above | c. |  |
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73.
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Find the indefinite integral of the following function and check the result by
differentiation. 
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74.
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The graph of f is shown below. For which value of x is  minimum? 
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75.
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Use the Quotient Rule to differentiate the function
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76.
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Evaluate the following definite integral by the limit definition.  a. |  | b. | 195 | c. | 661 | d. | 665 | e. |  |
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77.
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Find an equation of the line that is tangent to the graph of the function  and parallel to the line  .
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78.
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The graph of f is shown in the figure. Sketch a graph of the derivative
of f.
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79.
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Find the derivative of the function. 
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80.
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Use the graph of the function  given below to
estimate the open intervals on which the function is increasing or decreasing. 
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81.
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Find the vertical asymptotes (if any) of the function  .
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82.
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Evaluate the definite integral of the algebraic function.  Use a graphing utility to verify your results.
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83.
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Find the limit.
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84.
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Find the derivative of the algebraic function  .
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85.
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Use the alternative form of the derivative to find the derivative of the
function  at  .
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86.
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Find the differential dy of the function  .
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87.
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Determine the area of the given region.  
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88.
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Find the limit.
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89.
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Find the limit (if it exists).
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90.
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Find the derivative of the function  by the limit
process.
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91.
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Let  and  . Find the
limit.  a. | 4 | b. | –2 | c. | 9 | d. |  | e. |  |
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92.
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The graph of a function f is is shown below. Sketch the graph of the
derivative  . 
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93.
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Find the limit.  a. | 0 | b. |  | c. |  | d. | 1 | e. | does not exist |
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94.
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Find the derivative of the algebraic function  .
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95.
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Locate the absolute extrema of the function  on the
closed interval  . a. | absolute max:  ; absolute min:  | b. | absolute max:  ; no absolute min | c. | absolute max:  ; absolute min:  | d. | no absolute max;
absolute min:  | e. | no absolute max or
min |
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96.
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Find the differential dy of the function 
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97.
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Write the following limit as a definite integral on the interval [5 ,
10], where ci is any point in the ith
subinterval. 
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98.
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Complete the table and use the result to estimate the limit.  x | –0.1 | –0.01 | –0.001 | 0.001 | 0.01 | 0.1 | | | | | | | | | | | | | | |
a. |  | b. | 1 | c. |  | d. | 0.5 | e. | 0 |
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99.
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Find the second derivative of the function  .
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100.
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Let  Determine the following limit. (Hint:
Use the graph to calculate the limit.)   a. | 3 | b. | 5 | c. | 0 | d. | 4 | e. | does not
exist |
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101.
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Find the indefinite integral  .
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102.
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Find the lmit. 
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103.
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Find the derivative of the function.  .
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104.
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Find the sum given below.  a. | 185 | b. | 180 | c. | 175 | d. | 170 | e. | 207 |
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105.
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Find the indefinite integral  .
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