AP Calculus AB

Question 1

What is lim(x→3) (x² − 9)/(x − 3)?

Accepted Answer

6

Answer

Factor the numerator as (x+3)(x−3); canceling (x−3) leaves x+3, which equals 6 at x=3.

Question 2

Which condition is NOT required for a function f(x) to be continuous at x = a?

Accepted Answer

f′(a) exists

Answer

Differentiability implies continuity, but continuity does not require differentiability; only the three limit/value conditions are needed.

Question 3

What is lim(x→0) sin(x)/x?

Accepted Answer

1

Answer

This is a fundamental trigonometric limit — sin(x)/x approaches 1 as x approaches 0.

Question 4

If lim(x→2⁺) f(x) = 5 and lim(x→2⁻) f(x) = 3, what is lim(x→2) f(x)?

Accepted Answer

The limit does not exist

Answer

A two-sided limit exists only when both one-sided limits are equal; since 5 ≠ 3, the limit does not exist.

Question 5

What is lim(x→∞) (3x² + 2x)/(x² − 5)?

Accepted Answer

3

Answer

Dividing numerator and denominator by x² causes the lower-degree terms to vanish, leaving 3/1 = 3.

AP Practice Test