Limits & Continuity – AP Calculus AB

1. For a two-sided limit lim(x→a) f(x) to exist, which must be true?

f(a) must be defined Left and right limits must be equal f(a) must equal the limit The function must be continuous

2. A removable discontinuity means:

The limit does not exist at that point The limit exists but f(a) ≠ limit (or undefined) The function has a vertical asymptote Left and right limits differ

3. For f to be continuous at x = a, which THREE conditions must hold?

f(a) defined, lim exists, lim = f(a) f(a) defined, f is differentiable, f is integrable f(a) > 0, lim > 0, they are equal Limit exists from left only