Find the limit of $\frac{e^{\frac{1}{x}}-1}{x^{-1}}$ as $x$ approaches 0

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Learn how to solve limits by rationalizing problems step by step online. Find the limit of (e^(1/x)-1)/(x^(-1)) as x approaches 0. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Divide fractions \frac{e^{\frac{1}{x}}-1}{\frac{1}{x}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. Multiply the single term x by each term of the polynomial \left(e^{\frac{1}{x}}-1\right). Applying rationalisation.