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> If $$\lim\limits\_{x\to 0} \left(2+\frac{f(x)}{x^2}\right)^{\frac 1x} = e^2$$ and $f(x)=a\_0 + a\_1x+a\_2x^2...$, then prove that $$a\_2+|a\_3|=1\,.$$
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The function seems to be of the form $\infty^{\infty}$.

I don’t know how to start solving it, since it an indeterminate form I don’t know how to evaluate. Can I gain some insight into the question?

EDIT:-

$$y=\lim\_{x\to 0} (2+\frac{f(x)}{x^2})^{\frac 1x}$$
$$\log y = \lim\_{x\to 0} \frac 1x \log (2+\frac{f(x)}{x^2})$$
$$\log y = \frac 1x (1+\frac{f(x)}{x^2})=2$$