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Limits of Exponential Functions


Definition

Those are limits of expressions of the form $f(x)^{g(x)}$.

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Problems Solved

Find the limit $\lim_{x\to0}\left(arcsin\left(x\right)\right)^{\tan\left(x\right)}$
Find the limit $\lim_{x\to0}\left(1+\frac{5}{x}\right)^x$
Find the limit $\lim_{x\to0}\left(lnx\right)^x$
Find the limit $\lim_{x\to1}\left(x-1\right)^{\ln\left(x\right)}$
Find the limit $\lim_{x\to0}\left(\frac{1}{x}\right)^{\sin\left(x\right)}$
Find the limit $\lim_{x\to0}\left(\cot\left(x\right)\right)^{\ln\left(x\right)}$
Find the limit $\lim_{x\to0}\left(3x\right)^{2\:\sin\left(x\right)}$

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Related Topics

Limits by L'Hôpital's rule
Operations with Infinity
Limits by Direct Substitution
Limits by Factoring
Limits by Rationalizing

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