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AP Calculus AB/Unit 1: Limits and Continuity
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Continuity and Differentiability of a Piecewise Function

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Let kk be the function defined by k(x)={x2−1if x≤32x+1if x>3k(x) = \begin{cases} x^2 - 1 & \text{if } x \leq 3 \\ 2x + 1 & \text{if } x > 3 \end{cases}. Which of the following statements about kk at x=3x=3 is true?

A

kk is continuous and differentiable at x=3x = 3.

B

kk is continuous but not differentiable at x=3x = 3.

C

kk is defined but neither continuous nor differentiable at x=3x = 3.

D

kk is differentiable but not continuous at x=3x = 3.

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