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Rewrite the limit using the identity: $a^x=e^{x\ln\left(a\right)}$
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$\lim_{x\to\infty }\left(e^{\frac{1}{x^2}\ln\left(e^x+\frac{-1}{e^x}\right)}\right)$
Learn how to solve problems step by step online. Find the limit of (e^x+-1/(e^x))^(1/(x^2)) as x approaches infinity. Rewrite the limit using the identity: a^x=e^{x\ln\left(a\right)}. Multiplying the fraction by \ln\left(e^x+\frac{-1}{e^x}\right). 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)}}. The limit of a constant is just the constant.