Final Answer
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We could not solve this problem by using the method: Limits by Factoring
Split the fraction $\frac{e^x-e^{-x}}{x}$ in two fractions with common denominator $x$
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$\lim_{x\to0}\left(\frac{e^x}{x}+\frac{-e^{-x}}{x}\right)$
Learn how to solve limits by direct substitution problems step by step online. Find the limit (x)->(0)lim((e^x-e^(-x))/x). Split the fraction \frac{e^x-e^{-x}}{x} in two fractions with common denominator x. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. 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^x}{x}\right) by replacing all occurrences of x by 0.