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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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$\lim_{x\to0}\left(\sqrt{x}\right)\lim_{x\to0}\left(e^{\sin\left(\frac{\pi }{x}\right)}\right)$
Learn how to solve problems step by step online. Find the limit of x^1/2e^sin(pi/x) as x approaches 0. The limit of the product of two functions is equal to the product of the limits of each function. Evaluate the limit \lim_{x\to0}\left(\sqrt{x}\right) by replacing all occurrences of x by 0. Calculate the power \sqrt{0}. 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)}}.