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AP® Calculus AB-BC

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Difficult

Matching a Given Limit to a Function

APCALC-L5VD0K

For which of the following does $\lim \limits_{h \to 0} \frac{f(x+h)-f(x)}{h} \neq e^{-2x}?$

A

$f(x)=\ln (e^{2x})$

B

$f(x)=-\cfrac{1}{2e^{2x}}+5$

C

$f(x)=\cfrac{14e^{2x}-1}{2e^{2x}}$

D

$f(x)=- \left( \cfrac{1}{2}e^{-2x} \right) +1$