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

1. Find f (2) and f (x ) and determine if f is continuous at x = 2. (See Figure 5.4-1.)

Answer: f (2)=2, f (x )=4, and f is discontinuous at x = 2.



2. 
3. 

Answer: The limit is –3, since the polynomials in the numerator and denominator have the same degree.

4. 
5. 
6. 
7. 

Answer: The limit is –∞, since (x² – 25) approaches 0 through negative values.

8. Find the vertical and horizontal asymptotes of

Answer: The vertical asymptotes are x = ± 5, and the horizontal asymptote is y = 0, since f (x) = 0.

Practice problems for this concept can be found at Limits and Continuity Practice Problems for AP Calculus,