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Limits and Continuity Practice Problems for AP Calculus

based on 13 ratings
By — McGraw-Hill Professional
Updated on Oct 24, 2011

Review this concept at Limits and Continuity Rapid Review for AP Calculus.

Review the following concepts if needed:

Part A The use of a calculator is not allowed.

Find the limits of the following:

  1. The graph of a function f is shown in Figure 5.5-1.
  2. Which of the following statements is/are true?

    1. x =4 is not in the domain of f

Part B Calculators are allowed.

  1. Find the horizontal and vertical asymptotes of the graph of the function
  2. Limits and Continuity Practice Problems

  3. Find the limit: is the greatest integer of x.
  4. Find the points of discontinuity of the function
  5. For what value of k is the function
  6. Determine if is continuous at x =2. Explain why or why not.
  7. Given f (x ) as shown in Figure 5.5-2, find
    1. f (3)
    2. Is f (x ) continuous at x =3? Explain why or why not.
  8. A function f is continuous on [–2, 2] and some of the values of f are shown below:
  9. If f has only one root, r, on the closed interval [–2, 2], and r ≠ 0, then a possible value of b is

    1. –3
    2. –2
    3. –1
    4. 0
    5. 1

 

  1. Write an equation of the line passing through the point (2, – 4) and perpendicular to the line 3x – 2y =6.
  2. The graph of a function f is shown in Figure 5.6-1. Which of the following statements is/are true?
    1. x = 4 is not in the domain of f.
    2. does not exist.
  3. Find the horizontal and vertical asymptotes of
  4. Limits and Continuity Practice Problems

Solutions for these practice problems can be found at Limits and Continuity Solutions to Practice Problems for AP Calculus.

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