# CLEP Calculus: Study Guide & Test Prep Final Exam

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Question 1
1.
According to L'Hopital's rule, which of the following statements MUST be true for the equation shown below to hold?

A) f(x) and g(x) approach 0 or infinity

B) f'(C) does not equal 0

C) g'(x) does not equal 0

#### Question 2 2. How many zeroes does the derivative of this graph have?

#### Question 3 3. What is the derivative of y?

#### Question 4 4. What is the volume of a hemisphere with a radius of 3?

#### Question 5 5. The derivative below may have been calculated from which function f(x)?

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#### Question 6 6. Find f'(t) given the function f(t):

#### Question 7 7. Where is the global maximum for the function y=f(x) below between x=0 and x=2?

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Question 8
8.
Which of the following best describe(s) the derivative of a function?

a) It is the instantaneous rate of change.

b) It is the slope between any two points.

c) It is the tangent to the function.

#### Question 9 9. Find the following limit:

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Question 10
10.
__For these questions, I strongly recommend using either the CLEP calculator (found online) or one you use in class.__

Find x.

__For these questions, I strongly recommend using either the CLEP calculator (found online) or one you use in class.__

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#### Question 11 11. Consider the function f(x) below. At x = 2 is this function concave up, concave down, or an inflection point?

#### Question 12 12. What meaning does the derivative have?

#### Question 13 13. The derivative of the following graph is _____ at point C.

#### Question 14 14. What is the global minimum for the function y=f(x) below between x=0 and x=2?

#### Question 15 15. Which of the following illustrates the Fundamental Theorem of Calculus?

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#### Question 16 16. Solve the following differential equation for y=f(x) (assume that y is always positive).

#### Question 17 17. Which of the following might represent the shown Riemann sum for the area under the curve f(x) between x=0 and x=2?

#### Question 18 18. I have a discontinuous graph where I know that f(1) = 2 and f(5) = 20. Does the intermediate value theorem tell me that there will be a point between f(1) and f(5) that will equal 10?

#### Question 19 19. Find the derivative of f(x).

#### Question 20 20. Find the second derivative of f(x) shown below:

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#### Question 21 21. Solve the following differential equation for y=f(x).

#### Question 22 22. The average value for this continuous function over the shaded region is 2. According to the average value theorem, how many times does this function pass through the value 2?

#### Question 23 23. Where is y differentiable?

#### Question 24 24. Of the three limits shown below, which can be evaluated using L'Hopital's Rule?

#### Question 25 25. Evaluate the following integral. As a hint, you might want to simplify the fraction as shown.

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Question 26
26.
Which of the following functions are continuous?

I) f(x) = 1/(x-1),

II) f(x) = abs(x)-x,

III) f(x) = x^2/2

#### Question 27 27. What is the equation for the volume of this cone that extends from x=0 to x=A, given that h=x?

#### Question 28 28. Find z, the shaded area in the graph below.

#### Question 29 29. What is the length of y = x between x=3 and x=8?

#### Question 30 30. Find the derivative of y(t).

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#### Question 31 31. Find the derivative of p(t).

#### Question 32 32. If function f(x) is my upper boundary and function g(x) is my lower boundary from x=0 to x=2 and function h(x) my lower boundary from x=2 to x=5, what is my formula for finding the area between these functions?

#### Question 33 33. Solve the following differential equation for y=f(x).

#### Question 34 34. What is the one term left-sided Riemann Sum approximation for the integral below?

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Question 35
35.
What is the inverse function of f(*x*) = *x*/8 + *x* + 2?

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#### Question 36 36. What is the point-slope form of the equation that goes through the origin and has a slope of 1.5?

#### Question 37 37. In the following integral, 4 is defined as which of the following?

#### Question 38 38. Integrate the following.

#### Question 39 39. Find the derivative of f(x).

#### Question 40 40. Given the graph of f'(x) below, what can you say about f(x)?

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Question 41
41.
__For these questions, I strongly recommend using either the CLEP calculator (found online) or one you use in class.__

Evaluate:

(0.22+0.47)*2.33

__For these questions, I strongly recommend using either the CLEP calculator (found online) or one you use in class.__

#### Question 42 42. When you blow up a balloon, the time that it takes to blow it up depends on how much pressure the inlet air is under. (AKA, how hard you blow!) If the pressure is higher, the rate of change of the balloon volume _____ as a function of time.

#### Question 43 43. Use the graph to solve for z.

#### Question 44 44. What is the equation for the length of a curve following y=f(x) between x=a and x=b?

#### Question 45 45. Which of the following represents an equation for your bank balance as a function of time given a starting balance of $147 and an interest rate of 3%

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#### Question 46 46. Consider the region bound by the x-axis, the y-axis, and f(x) between 0 and 4. What is the area of this region?

#### Question 47 47. You can enclose a rectangular yard with a fence. The length of the longest side of the fence is going to be 2 times the length of the shortest side of the fence. Write the equation for the perimeter of the fence.

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Question 48
48.
__For these questions, I strongly recommend using either the CLEP calculator (found online) or one you use in class.__

Where is the maximum value of f(x) between 0 and pi?

__For these questions, I strongly recommend using either the CLEP calculator (found online) or one you use in class.__

#### Question 49 49. What is the equation for the volume of this cone that extends from x=0 to x=A, given that h=x?

#### Question 50 50. Simplify:

#### CLEP Calculus: Study Guide & Test Prep Final Exam Instructions

Choose your answers to the questions and click 'Next' to see the next question. You can skip questions if you would like and come back to them later with the "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. You will lose your work if you close or refresh this page. Good luck!