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Step-by-step Solution

Find the limit of $x^2e^x$ as $x$ approaches $+\infty$

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Answer

$\frac{+\infty^2e^{+\infty}}{1+e^{3+\infty}}$

Step-by-step explanation

Problem to solve:

$\lim_{x\to+\infty}\left(\frac{x^2e^x}{1+e^{3x}}\right)$
1

Evaluating the limit when $x$ tends to $+\infty$

$\frac{+\infty^2e^{+\infty}}{1+e^{3+\infty}}$

Answer

$\frac{+\infty^2e^{+\infty}}{1+e^{3+\infty}}$
$\lim_{x\to+\infty}\left(\frac{x^2e^x}{1+e^{3x}}\right)$

Main topic:

Limits by direct substitution

Time to solve it:

~ 0.04 seconds