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We could not solve this problem by using the method: Limits by Factoring
Split the fraction $\frac{e^{2x}-1}{\sin\left(x\right)}$ in two fractions with common denominator $\sin\left(x\right)$
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$\lim_{x\to0}\left(\frac{e^{2x}}{\sin\left(x\right)}+\frac{-1}{\sin\left(x\right)}\right)$
Learn how to solve limits by direct substitution problems step by step online. Find the limit (x)->(0)lim((e^(2x)-1)/sin(x)). Split the fraction \frac{e^{2x}-1}{\sin\left(x\right)} in two fractions with common denominator \sin\left(x\right). The limit of a sum of two or more functions is equal to the sum of the limits of each function: \displaystyle\lim_{x\to c}(f(x)\pm g(x))=\lim_{x\to c}(f(x))\pm\lim_{x\to c}(g(x)). Evaluate the limit \lim_{x\to0}\left(\frac{e^{2x}}{\sin\left(x\right)}\right) by replacing all occurrences of x by 0. Multiply 2 times 0.