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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!

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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