Question
Calculate the given limit.$\lim _{x \rightarrow 0} \frac{\operatorname{arcsinh}(x)-\arcsin (x)}{x^{3}}$
Step 1
The Taylor series expansion for $\operatorname{arcsinh}(x)$ around $x=0$ is: \[\operatorname{arcsinh}(x) = x - \frac{x^{3}}{6} + O(x^{5})\] The Taylor series expansion for $\arcsin (x)$ around $x=0$ is: \[\arcsin (x) = x + \frac{x^{3}}{6} + O(x^{5})\] Show more…
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