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Calculus AB Flashcards

7 cards from real AP practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 7 Calculus AB flashcards as text

  1. What is lim(x→3) (x² − 9)/(x − 3)?

    Answer: 6

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

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

    Answer: f′(a) exists

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

  3. What is lim(x→0) sin(x)/x?

    Answer: 1

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

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

    Answer: The limit does not exist

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

  5. What is lim(x→∞) (3x² + 2x)/(x² − 5)?

    Answer: 3

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

  6. Which function has a removable discontinuity at x = 2?

    Answer: f(x) = (x² − 4)/(x − 2)

    Factoring gives (x+2)(x−2)/(x−2) = x+2 for x ≠ 2, leaving a hole (removable discontinuity) at x = 2.

  7. What is lim(x→0) (1 − cos x)/x²?

    Answer: 1/2

    Applying L'Hôpital's rule twice (or using the half-angle identity) yields 1/2.