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

AP Calculus ABmediummcq1 pt

$\lim_{h\to 0}\dfrac{(3+h)^2-9}{h}=$

A.

6

B.

0

C.

9

D.Does not exist

Explanation

Core Concept

Expand: $(3+h)^2-9=9+6h+h^2-9=6h+h^2$ . Dividing by $h$ gives $6+h$ , which approaches $6$ . This limit is the derivative of $x^2$ at $x=3$ .

Correct Answer

A $6$

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