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\question % workshop bank Ch. 4 -> esergel41
Evaluate $\displaystyle \lim_{x \to 0} \frac{\sin(x^3)}{\sin^3(x)}$ in two ways.

\begin{parts}

\part First, use L'Hospital's rule. You may have to apply it more than once. Don't forget to stop once you reach a form which is not indeterminate.

\part Second, use the identity $\displaystyle \lim_{u \to 0} \frac{\sin(u)}{u} = 1$ with $u=x$ and $u=x^3$.\\ (Note that $x^3 \to 0$ exactly when $x \to 0$.)

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