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
- Find f (2) and f (x ) and determine if f is continuous at x = 2. (See Figure 5.4-1.)
- Find the vertical and horizontal asymptotes of
Answer: f (2)=2, f (x )=4, and f is discontinuous at x = 2.
Answer: The limit is –3, since the polynomials in the numerator and denominator have the same degree.
Answer: The limit is –∞, since (x2 – 25) approaches 0 through negative values.
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,