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Step-by-step Solution
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Apply the formula: $\lim_{x\to c}\left(a^b\right)$$=\lim_{x\to c}\left(e^{b\ln\left(a\right)}\right)$, where $a=\sin\left(x\right)$, $b=x$ and $c=0$
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$\lim_{x\to0}\left(e^{x\ln\left(\sin\left(x\right)\right)}\right)$
Learn how to solve problems step by step online. (x)->(0)lim(sin(x)^x). Apply the formula: \lim_{x\to c}\left(a^b\right)=\lim_{x\to c}\left(e^{b\ln\left(a\right)}\right), where a=\sin\left(x\right), b=x and c=0. Apply the formula: \lim_{x\to c}\left(a^b\right)={\left(\lim_{x\to c}\left(a\right)\right)}^{\lim_{x\to c}\left(b\right)}, where a=e, b=x\ln\left(\sin\left(x\right)\right) and c=0. Apply the formula: \lim_{x\to c}\left(a\right)=a, where a=e and c=0. Rewrite the product inside the limit as a fraction.
