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The power of a quotient is equal to the quotient of the power of the numerator and denominator: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$
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$\lim_{x\to0}\left(\left(1+\sqrt{2x}\right)^{\frac{\sqrt{2}}{\sqrt{x}}}\right)$
Learn how to solve problems step by step online. Find the limit of (1+(2x)^1/2)^(2/x)^1/2 as x approaches 0. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. Calculate the power \sqrt{2}. 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)}}. Evaluate the limit \lim_{x\to0}\left(\frac{\sqrt{2}}{\sqrt{x}}\right) by replacing all occurrences of x by 0.