I have an exercise of finding a real number "a" and limit of $$\lim_{x\to0}\frac{e^{-x^2}-(1+ax^2)}{x^4}$$
I have no idea what should I do, can someone help me solve this step-by-step? Thank you in advance.
2026-04-01 15:26:06.1775057166
Find convergence and limit of $\lim_{x\to0}\frac{e^{-x^2}-(1+ax^2)}{x^4}$
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Hint: Use the fact that$$e^{-x^2}=1-x^2+\frac{x^4}2-\frac{x^6}{3!}+\cdots$$