Apentix/AP Calculus AB/Unit 1: Limits and Continuity/Question

AP Calculus ABhardmcq1 pt

$\lim_{x\to 1}\dfrac{x^3-1}{x-1}=$

A.

1

B.

0

C.Does not exist

D.

3

Explanation

Core Concept

Factor the numerator: $x^3-1=(x-1)(x^2+x+1)$ . Cancelling $x-1$ leaves $x^2+x+1$ , which approaches $1+1+1=3$ .

Correct Answer

D $3$

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