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AP® Calculus AB-BC

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Difficult

Factoring with $e$

APCALC-SUDEUG

Find the limit below:

$$ \lim_{x\to\ln3}\cfrac{e^{3x}-27}{e^{2x}-9} $$

A

$\cfrac{9}{2}$

B

$3$

C

$-3$

D

Nonexistent.