Final Answer
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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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${\left(\lim_{x\to0}\left(\frac{1+\tan\left(x\right)}{1+\sin\left(x\right)}\right)\right)}^{\lim_{x\to0}\left(\frac{1}{\sin\left(x\right)}\right)}$
Learn how to solve problems step by step online. Find the limit of ((1+tan(x))/(1+sin(x)))^(1/sin(x)) as x approaches 0. 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\to0}\left(\frac{1}{\sin\left(x\right)}\right) by replacing all occurrences of x by 0. The sine of 0 equals . An expression divided by zero tends to infinity.