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We could not solve this problem by using the method: Limits by Factoring
Rewrite the limit using the identity: $a^x=e^{x\ln\left(a\right)}$
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$\lim_{x\to0}\left(e^{\tan\left(x\right)\ln\left(x+\sin\left(x\right)\right)}\right)$
Learn how to solve problems step by step online. Find the limit of (x+sin(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(x+\sin\left(x\right)\right)}\right) by replacing all occurrences of x by 0. The sine of 0 equals 0. \ln(0) grows unbounded towards minus infinity.