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The limit of the product of a function and a constant is equal to the limit of the function, times the constant: $\displaystyle \lim_{t\to 0}{\left(at\right)}=a\cdot\lim_{t\to 0}{\left(t\right)}$
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$2\lim_{x\to\infty }\left(x^2e^{-\sqrt{x}}\right)$
Learn how to solve limits to infinity problems step by step online. Find the limit of 2x^2e^(-x^1/2) as x approaches infinity. The limit of the product of a function and a constant is equal to the limit of the function, times the constant: \displaystyle \lim_{t\to 0}{\left(at\right)}=a\cdot\lim_{t\to 0}{\left(t\right)}. Evaluate the limit \lim_{x\to\infty }\left(x^2e^{-\sqrt{x}}\right) by replacing all occurrences of x by \infty . Infinity to the power of any positive number is equal to infinity, so \sqrt{\infty }=\infty. Apply the formula: n^{- \infty }=0, where n=e.