I've thought of the sandwich theorem but can't find anything to squeeze it in !
2026-04-06 16:37:45.1775493465
$\lim_{x\to 0}\frac{(\sin{4x})(-\cos{x})}{x}$ without l'Hôpital's Rule?
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Let's build our way up to the answer.
Step 1. Find the value of $$\lim_{x\to 0} \frac{\sin 4x}{4x}$$
Step 2. Use the result above to find the value of $$\lim_{x\to 0} \frac{\sin 4x}{x}$$
Step 3. Finally use the result above to find the value of $$\lim_{x\to 0} \left(\frac{\sin 4x}{x}\cdot-\cos(x)\right)$$
Can you take it from there?