Final Answer
Step-by-step Solution
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The limit of the product of two functions is equal to the product of the limits of each function
If $n>0$, then $\lim_{x\to\infty}(x^n)=\infty$
Evaluate the limit $\lim_{x\to\infty }\left(\frac{1}{e^x}\right)$ 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 $e$
Any expression divided by infinity is equal to zero
$0\cdot\infty$ is an indeterminate form