Limits and Continuity Practice Problems for AP Calculus

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

Review the following concepts if needed:

• Definition and Properties of Limits for AP Calculus
• Evaluating Limits for AP Calculus
• One-Sided Limits for AP Calculus
• Squeeze Theorem for AP Calculus
• Infinite Limits for AP Calculus
• Limits at Infinity for AP Calculus
• Horizontal and Vertical Asymptotes for AP Calculus
• Continuity of a Function for AP Calculus

Part A The use of a calculator is not allowed.

Find the limits of the following:

1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11. 
12. The graph of a function f is shown in Figure 5.5-1.

Which of the following statements is/are true?

1. 
2. 
3. x =4 is not in the domain of f

Part B Calculators are allowed.

13. Find the horizontal and vertical asymptotes of the graph of the function





14. Find the limit: is the greatest integer of x.
15. Find the points of discontinuity of the function
16. For what value of k is the function
17. Determine if is continuous at x =2. Explain why or why not.
18. Given f (x ) as shown in Figure 5.5-2, find
    1. f (3)
    2. 
    3. 
    4. 
    5. Is f (x ) continuous at x =3? Explain why or why not.



19. A function f is continuous on [–2, 2] and some of the values of f are shown below:



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
20. 

21. Write an equation of the line passing through the point (2, – 4) and perpendicular to the line 3x – 2y =6.
22. The graph of a function f is shown in Figure 5.6-1. Which of the following statements is/are true?
    1. 
    2. x = 4 is not in the domain of f.
    3. does not exist.
23. 
24. 
25. Find the horizontal and vertical asymptotes of

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