$\lim_{x\to \infty}\dfrac{\cos(3x)}{e^{8x}}$
The answer is $0$. Why is the answer $0$? The top oscillates between $-1$ and $1$ and the bottom becomes huge, but since the top is oscillating, shouldn't the answer be DNE (does not exist)?
2026-03-28 01:13:36.1774660416
Question about $\lim_{x\to \infty}\frac{\cos(3x)}{e^{8x}}$
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Hint: Notice that for all $x \in \mathbb R$, we have that: $$ \frac{-1}{e^{8x}} \leq \frac{\cos(3x)}{e^{8x}} \le \frac{1}{e^{8x}} $$