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The limit of the product of two functions is equal to the product of the limits of each function
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$\lim_{x\to\infty }\left(\frac{1}{x^{-1}}\right)\lim_{x\to\infty }\left(\sin\left(e^{-x}\right)\right)$
Learn how to solve problems step by step online. Find the limit of sin(e^(-x))/(x^(-1)) as x approaches infinity. The limit of the product of two functions is equal to the product of the limits of each function. Because sine is a continuous function, we can bring the limit inside of the sine. Apply the power rule of limits: \displaystyle{\lim_{x\to a}f(x)^{g(x)} = \lim_{x\to a}f(x)^{\displaystyle\lim_{x\to a}g(x)}}. The limit of a constant is just the constant.