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Evaluate the limit $\lim_{x\to\infty }\left(xe^x\right)$ by replacing all occurrences of $x$ by $\infty $
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$\infty \cdot e^{\infty }$
Learn how to solve limits to infinity problems step by step online. Find the limit of xe^x as x approaches infinity. Evaluate the limit \lim_{x\to\infty }\left(xe^x\right) by replacing all occurrences of x by \infty . Apply a property of infinity: k^{\infty}=\infty if k>1. In this case k has the value e. If you multiply a very large number by another very large number, you get an even bigger number, so infinity times infinity equals infinity: \infty\cdot\infty=\infty.