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Evaluate the limit $\lim_{x\to1}\left(\left(1+3\ln\left(x\right)\right)^{\frac{1}{\sin\left(1-x\right)}}\right)$ by replacing all occurrences of $x$ by $1$
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$\left(1+3\ln\left(1\right)\right)^{\frac{1}{\sin\left(1-1\cdot 1\right)}}$
Learn how to solve limits of exponential functions problems step by step online. Find the limit (x)->(1)lim((1+3ln(x))^(1/(sin(1-x))). Evaluate the limit \lim_{x\to1}\left(\left(1+3\ln\left(x\right)\right)^{\frac{1}{\sin\left(1-x\right)}}\right) by replacing all occurrences of x by 1. Simplifying, we get. Apply the formula for limits that result in the indeterminate form 1^{\infty}, which is as follows: \lim_{x\to a}f(x)^{g(x)}=\lim_{x\to a}e^{\left[g(x)\cdot\left(f(x)-1\right)\right]}. Multiplying the fraction by 3\ln\left(x\right).