Find the limit of $$\begin{equation*} \lim_{x \rightarrow 0} \frac{|\sin x||\cos x|}{x} \end{equation*},$$
What is the value of $|\sin x|$ & $|\cos x|$?
Could anyone help me please?
2026-04-06 21:54:35.1775512475
Find $\lim_{x \rightarrow 0} \frac{|\sin x||\cos x|}{x}$
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Use the fact that when $x \approx 0$, $\sin x \sim x$.
Calculating the left limit, $${|\sin x \ | \over x} \approx -1,$$ and for the right limit, $${|\sin x \ | \over x} \approx 1.$$
Can you calculate the limits now? Does the two-sided limit exist?