Find the limit of $\left(\frac{1-\cos\left(x\right)\sqrt{\cos\left(2x\right)}}{\tan\left(x\right)^2}\right)^{\frac{1}{x^2}}$ as $x$ approaches 0

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Final answer to the problem

indeterminate

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Evaluate the limit $\lim_{x\to0}\left(\left(\frac{1-\cos\left(x\right)\sqrt{\cos\left(2x\right)}}{\tan\left(x\right)^2}\right)^{\frac{1}{x^2}}\right)$ by replacing all occurrences of $x$ by $0$

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

$\left(\frac{1-\cos\left(0\right)\sqrt{\cos\left(2\cdot 0\right)}}{\tan\left(0\right)^2}\right)^{\frac{1}{0^2}}$

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Learn how to solve limits of exponential functions problems step by step online. Find the limit of ((1-cos(x)cos(2x)^(1/2))/(tan(x)^2))^(1/(x^2)) as x approaches 0. Evaluate the limit \lim_{x\to0}\left(\left(\frac{1-\cos\left(x\right)\sqrt{\cos\left(2x\right)}}{\tan\left(x\right)^2}\right)^{\frac{1}{x^2}}\right) by replacing all occurrences of x by 0. Multiply 2 times 0. Calculate the power 0^2. The cosine of 0 equals 1.

Final answer to the problem

indeterminate

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Function Plot

Plotting: $\left(\frac{1-\cos\left(x\right)\sqrt{\cos\left(2x\right)}}{\tan\left(x\right)^2}\right)^{\frac{1}{x^2}}$

Main Topic: Limits of Exponential Functions

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

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