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L'Hôpital's Rule

When you've got a limit that looks like 0/0 or ∞/∞, L'Hôpital's rule can often find its value -- and make it clear that not all infinities are equal!

L'Hopital's Rule

Evaluate $\lim_{x \to \infty} \frac{e^{-x}}{x^{-15}}.$

Evaluate $\lim_{x \to 0} \frac{6x+\tan x}{\sin x}.$

Evaluate $$\displaystyle \lim_{x \to 0} \frac{e^{26x}-1}{\sin x}$$.

Evaluate $$\displaystyle \lim_{x \to 1} \frac{x^{14}+8x-9}{x-1}$$.

Evaluate $\lim_{x \to 0} \frac{\tan 19x}{\tan 10x}.$

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