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Study Resources (Calculus)

16.Find the constant a such that the function is continuous on the entire real line.   a. b. c. d. e.   17.Find the value of c guaranteed by the Intermediate Value Theorem.   a. b. c. d. e.   18.Find the value of c guaranteed by the Intermediate Value Theorem.   a. b. c. d. e.   19.A long distance phone service charges $  for the first minutes and $ for each additional.
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6.Find the derivative of the following function using the limiting process.   a. –4 b. c. d. e.   7.Find the derivative of the following function using the limiting process.   a. b. c. d. e.   8.Find the derivative of the following function using the limiting process.   a. b. c. d. e.   9.Find the derivative of the following function using the limiting process.   a. b. c. d. e.   10.Find the derivative of the function using the limiting.
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16.Suppose that . Find the following limit.   a. 2 b. 125 c. 8 d. 0 e. 15   17.Suppose that . Find the following limit.   a. –5 b. 15 c. –15 d. e. 3   18.Find the following limit (if it exists). Write a simpler function that agrees with the given function at all but one point.   a. 40 b. –24 c. 24 d. –40 e.   19.Find the limit (if it exists).   a. b. c. –32 d. –8 e.   20.Find the limit (if it exists).   a. 6 b. c. d. e. .       .
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  6.Use implicit differentiation to find   a. b. c. d. e.   7.Find by implicit differentiation.   a. b. c. d. e.   8.Find by implicit differentiation.   a. b. c. d. e.   9.Find by implicit differentiation.   a. b. c. d. e.   10.Find  by implicit differentiation given that . Use the original equation to simplify your answer.   a. b. c. d. e.     .
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6.Use the quotient rule to differentiate the following function and evaluate .   a. b. c. d. e.   7.Find the derivative of the algebraic function .   a. b. c. d. e.   8.Use the Product Rule to differentiate .   a. b. c. d. e.   9.Use the Product Rule to differentiate.   a. b. c. d. e.   10.Use the Quotient Rule to differentiate the function .   a. b. c. d. e.       .
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  26.Use logarithmic differentiation to find the derivative of .   a. b. c. d. e.   27.Use logarithmic differentiation to find .     a. b. c. d. e.   28.Use logarithmic differentiation to find .   a. b. c. d. e.   29.Differentiate with respect to t (x and y are functions of t).   a. b. c. d. e.   30.Differentiate with respect to t (x and y are functions of t).   a. b. c. d. e.         .
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16.Find an equation of the line that is tangent to the graph of the function and parallel to the line .   a. b. c. d. e.   17.The graph of the function  f is given below. Select the graph of .   a. d. b. e. c.   18.Identify the graph which has the following characteristics. Graph 1                                                  Graph 2 Graph 3                                                   Graph 4   a. Graph 2 b. Graph 3 c. Graph.
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6.Find the limit (if it exists).   a. b. c. d. e.   7.Find the limit (if it exists). Note that represents the greatest integer function.   a. b. c. d. e.   8.Find the limit (if it exists). Note that represents the greatest integer function.   a. b. c. d. e.   9.Discuss the continuity of the function .   a. b. c. d. e.   10.Find the x-values (if any) at which the function  is not continuous..
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11.A ring has a inner circumference of 10 centimeters. What is the radius of the ring? Round your answer to four decimal places.   a. 0.7958 centimeter b. 3.1831 centimeters c. 1.5915 centimeters d. 1.7841 centimeters e. 10.1321 centimeters   12.A ring has a inner circumference of 9 centimeters. If the ring's inner circumference can vary between 8 centimeters and 10 centimeters how.
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6.Determine the following limit. (Hint: Use the graph to calculate the limit.)   a. 6 b. 1 c. 5 d. 4 e. does not exist   7.Determine the following limit. (Hint: Use the graph to calculate the limit.)   a. 5 b. 1 c. 0 d. 4 e. does not exist   8. Let  Determine the following limit. (Hint: Use the graph to calculate the limit.) a. 5 b. 4 c. 3 d. 0 e. does not exist   9.Let Determine the following limit. (Hint: Use the graph.
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  21.Find the derivative of the function .   a. b. c. d. e.   22.Find the derivative of the function  .   a. b. c. d. e.   23.Find the derivative of the function .   a. b. c. d. e.   24.Find the second derivative of the function.   a. b. c. d. e.   25.Find the second derivative of the function .   a. b. c. d. e.     .
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MULTIPLE CHOICE 1.Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution. Find the distance traveled in 16 seconds by.
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MULTIPLE CHOICE 1.Complete the table and use the result to estimate the limit.   x 2.9 2.99 2.999 3.001 3.01 3.1               a. 0.525000 b. 0.275000 c. –0.100000 d. 0.400000 e. –0.475000   2.Complete the table and use the result to estimate the limit.   x 6.9 6.99 6.999 7.001 7.01 7.1                 a. –0.062500 b. 0.067500 c. –0.192500 d. 0.047500 e. –0.172500   3.Complete the table and use the result to estimate the limit.   x –10.1 –10.01 –10.001 –9.999 –9.99 –9.9               a. 0.974745 b. –1.099745 c. –1.224745 d. 1.058078 e. 1.224745   4.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. 0 c. 1 d. 0.5 e.   5.Complete the table and use the result to estimate.
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11.Find the derivative of the function .   a. b. c. d. e.   12.Find the derivative of the function . Simplify your answer.   a. b. c. d. e.   13.Find the derivative of the function.  .   a. b. c. d. e.   14.Find the derivative of the trigonometric function .   a. b. c. d. e.   15.Find an equation of the tangent line to the graph of f at the given point.   a. b. c. d. e.       .
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6.Find the derivative of the function .   a. b. c. d. e.   7.Find the derivative of the function .   a. b. c. d. e.   8.Find the slope of the graph of the function at the given value. when   a. b. c. d. e.   9.Find the slope of the graph of the function at the given value. when   a. b. c. d. e.   10.Find the slope of the graph of the function at.
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11.Find the following limit if it exists:. Use when appropriate.   a. b. c. d. e.   12.Find the limit (if it exists).   a. b. c. d. e.   13.Use a graphing utility to graph the function and determine the one-sided limit .   a. b. c. 0 d. e. 8   14.Use a graphing utility to graph the function and determine the following one-sided limit.   a. b. c. d. e.       .
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MULTIPLE CHOICE 1.Find the derivative of the function.   a. b. c. d. e.   2.Find the derivative of the function.   a. b. c. d. e.   3.Use the rules of differentiation to find the derivative of the function .   a. b. c. d. e.   4.Find the derivative of the function .   a. b. c. d. e.   5.Use the rules of differentiation to find the derivative of the function .   a. b. c. d. e.       .
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MULTIPLE CHOICE 1.What is the domain of the function ?   a. b. c. d. e.   2.What is the domain of the function ?   a. b. c. d. e.   3.Write the following expression as a logarithm of a single quantity.   a. b. c. d. e.   4.Write the following expression as a logarithm of a single quantity.     a. b. c. d. e.       .
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MULTIPLE CHOICE 1.Find the derivative of the algebraic function .   a. b. c. d. e.   2.Find the derivative of the function.   a. b. c. d. e.   3.Find the derivative of the function.   a. b. c. d. e.   4.Find the derivative of the function.   a. b. c. d. e.   5.Find the derivative of the function.   a. b. c. d. e.     .
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11.Find the x-values (if any) at which is not continuous. a. b. c. d. e.   12.Find the x-values (if any) at which the function is not continuous. Which of the discontinuities are removable?   a. 10 and -, removable b. discontinuous everywhere c. continuous everywhere d. 10 and -, not removable e. 0, removable   13.Find the x-values (if any) at which the function is not continuous..
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11.Find the slope of the graph of the function at the given value.   at   a. b. c. d. e.   12.Find the derivative of the function .   a. b. c. d. e.   13.Find the derivative of the function .   a. b. c. d. e.   14.Find the slope-intercept equation of the line tangent to the graph of  when   a. b. c. d. e.   15.Determine all values of , (if any), at which the.
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6.Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution. Find the area of the shaded region.   a. calculus , 11 b. precalculus.
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  16.Use implicit differentiation to find at the point .   a. b. c. d. e.   17.Find the slope of the tangent line at the given point . Round your answer to two decimal places.   a. 0.67 b. 2.00 c. 1.00 d. 1.67 e. 3.00   18.Find an equation of the tangent line to the graph of the function given below at the given point. (The coefficients below are.
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MULTIPLE CHOICE 1.Find by implicit differentiation.     a. b. c. d. e.   2.Find by implicit differentiation.   a. b. c. d. e.   3.Find by implicit differentiation given that .   a. b. c. d. e.   4.Find by implicit differentiation.   a. b. c. d. e.   5.Find by implicit differentiation given that .   a. b. c. d. e.     .
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MULTIPLE CHOICE 1.Determine whether approaches or as x approaches from the left and from the right by completing the tables below.   –3.1 –3.01 –3.001           –2.999 –2.99 –2.9 –2.5           a. b. c. d.   2.Find all the vertical asymptotes (if any) of the graph of the function   a. b. c. d. e. no vertical asymptotes   3.Find the vertical asymptotes (if any) of the function .   a. b. c. d. e.   4.Find all the.
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MULTIPLE CHOICE 1.Find the derivative of the algebraic function . a. b. c. d. e.   2.Use the Product Rule to differentiate . a. b. c. d. e.   3.Find the derivative of the function .   a. b. c. d. e.   4.Use the Quotient Rule to differentiate the function .   a. b. c. d. e.   5.Use the Quotient Rule to differentiate the function .   a. b. c. d. e.       .
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11.Let and . Find the limits.   a. b. c. – d. e.   12.Suppose that and . Find the following limit.   a. b. –10 c. –3 d. –23 e.   13.Suppose that and . Find the following limit.   a. 10 b. –5 c. –25 d. –15 e. 150   14.Suppose that and . Find the following limit.   a. 21 b. c. –21 d. e.   15.Suppose that and . Find the following limit.   a. –11 b. –8 c. 33 d. –14 e.       .
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16.Determine all values of , (if any), at which the graph of the function has a horizontal tangent.   a. b. c. d. e. The graph has no horizontal tangents.   17.Determine all values of , (if any), at which the graph of the function has a horizontal tangent.   a. b. c. d. e. The graph has no horizontal tangents.   18.Suppose the position function for a.
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  11.Use implicit differentiation to find .     a. b. c. d. e.   12.Use implicit differentiation to find .   a. b. c. d. e.   13.Evaluate for the equation at the given point . Round your answer to two decimal places.   a. b. c. d. e.   14.Evaluate for the equation at the given point . Round your answer to two decimal places.   a. b. c. d. e.   15.Evaluate for the equation .
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