If , where , then the minimum value of…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

If

\lim_{x\to0}\frac{\left(\tan\left(\frac{\pi}{4}+x\right)\right)^{\frac1x}-e^2}{x^2}=\left(\frac{p}{q}\right)e^2

, where

p,q\in\mathbb{N}

, then the minimum value of

p+q

is (a)

5

(b)

6

(c)

7

(d)

9

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