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:
- The graph of a function f is shown in Figure 5.5-1.
- x =4 is not in the domain of f
Which of the following statements is/are true?
Part B Calculators are allowed.
- Find the horizontal and vertical asymptotes of the graph of the function
- Find the limit: is the greatest integer of x.
- Find the points of discontinuity of the function
- For what value of k is the function
- Determine if is continuous at x =2. Explain why or why not.
- Given f (x ) as shown in Figure 5.5-2, find
- f (3)
- Is f (x ) continuous at x =3? Explain why or why not.
- 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
- Write an equation of the line passing through the point (2, – 4) and perpendicular to the line 3x – 2y =6.
- The graph of a function f is shown in Figure 5.6-1. Which of the following statements is/are true?
- x = 4 is not in the domain of f.
- does not exist.
- 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.