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Find the limit of $\arcsin\left(x\right)^{\tan\left(x\right)}$ as $x$ approaches 0

Step-by-step Solution

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Final answer to the problem

indeterminate

Step-by-step Solution

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  • Integrate by partial fractions
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Rewrite the limit using the identity: $a^x=e^{x\ln\left(a\right)}$

$\lim_{x\to0}\left(e^{\tan\left(x\right)\ln\left(\arcsin\left(x\right)\right)}\right)$

Learn how to solve limits of exponential functions problems step by step online.

$\lim_{x\to0}\left(e^{\tan\left(x\right)\ln\left(\arcsin\left(x\right)\right)}\right)$

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Learn how to solve limits of exponential functions problems step by step online. Find the limit of arcsin(x)^tan(x) as x approaches 0. Rewrite the limit using the identity: a^x=e^{x\ln\left(a\right)}. Evaluate the limit \lim_{x\to0}\left(e^{\tan\left(x\right)\ln\left(\arcsin\left(x\right)\right)}\right) by replacing all occurrences of x by 0. Calculating the tangent of 0 degrees. Calculating the arcsine of 0.

Final answer to the problem

indeterminate

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Function Plot

Plotting: $\arcsin\left(x\right)^{\tan\left(x\right)}$

Main Topic: Limits of Exponential Functions

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

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