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Applying the trigonometric identity: $\cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}$
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$\lim_{x\to0}\left(\frac{e^{\frac{1}{x}}}{\frac{\cos\left(x\right)}{\sin\left(x\right)}}\right)$
Learn how to solve limits by direct substitution problems step by step online. Find the limit (x)->(0)lim((e^(1/x))/cot(x)). Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}. Divide fractions \frac{e^{\frac{1}{x}}}{\frac{\cos\left(x\right)}{\sin\left(x\right)}} 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}. Evaluate the limit \lim_{x\to0}\left(\frac{e^{\frac{1}{x}}\sin\left(x\right)}{\cos\left(x\right)}\right) by replacing all occurrences of x by 0. The sine of 0 equals .