Calculate. $$\lim _{x \rightarrow 0} \frac{\cos x-1+x^{2} / 2}{x^{4}}$$
Added by Anna S.
Step 1
First, we can simplify the numerator by using the Taylor series expansion of cosine: $$\cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \cdots$$ So, we have: $$\cos x - 1 + \frac{x^2}{2} = -\frac{x^4}{4!} + \frac{x^6}{6!} - \cdots$$ Show more…
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