# Let's push the limits!

Calculus Level 5

$\large \lim_{x \to 0} \dfrac{(1+x)^{\frac{1}{x}}-e+ \frac{1}{2} ex}{x^2 (1+x)^{\frac{1}{x}}}$

If the limit above exists and is of the form $$\dfrac ab$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a+b.$$

If however, the limit doesn't exist or is irrational, enter 666 as your answer.

Clarification: $$e\approx 2.71828$$ denotes Euler's number.

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