Find the limit of 2xe^(1/x) as x approaches 0

 Exercise

\lim_{x\to0}\left(2xe^{\frac{1}{x}}\right)

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Evaluate the limit $\lim_{x\to0}\left(2xe^{\frac{1}{x}}\right)$ by replacing all occurrences of $x$ by $0$

2\cdot 0\sqrt[0]{e}

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Multiply $2$ times $0$

0\sqrt[0]{e}

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An expression divided by zero tends to infinity

0\cdot e^{\infty }

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Apply a property of infinity: $k^{\infty}=\infty$ if $k>1$ . In this case $k$ has the value $e$

0\cdot \infty

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$0\cdot\infty$ is an indeterminate form

indeterminate

indeterminate

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