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Apply the power rule of limits: $\displaystyle{\lim_{x\to a}f(x)^{g(x)} = \lim_{x\to a}f(x)^{\displaystyle\lim_{x\to a}g(x)}}$
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${\left(\lim_{x\to1}\left(x\right)\right)}^{\lim_{x\to1}\left(\frac{1}{x^2-1}\right)}$
Learn how to solve problems step by step online. Find the limit of x^(1/(x^2-1)) as x approaches 1. Apply the power rule of limits: \displaystyle{\lim_{x\to a}f(x)^{g(x)} = \lim_{x\to a}f(x)^{\displaystyle\lim_{x\to a}g(x)}}. Evaluate the limit \lim_{x\to1}\left(\frac{1}{x^2-1}\right) by replacing all occurrences of x by 1. Calculate the power 1^2. Subtract the values 1 and -1.