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## Homework Statement

Find the limit.

[tex]\lim_{x\rightarrow -\infty} x^2e^x[/tex]

## Homework Equations

L'Hospital's Rule.

## The Attempt at a Solution

I rewrite the limit:

[tex]\lim_{x\rightarrow -\infty} \frac{e^x}{\frac{1}{x^2}}[/tex]

applying L'Hospital's Rule:

[tex]\lim_{x\rightarrow -\infty} \frac{e^x}{-2(\frac{1}{x^3})}[/tex]

But the numerator and denominator still go to zero...If I keep applying L'Hospital's Rule, I still won't get anywhere. It looks like x's exponent will continue to grow; then if I put the x term back in the numerator, it would seem like the x term would overcome e^x, and the limit would go to infinity. However, I graphed the function, and it seems to go to zero. What am I doing wrong?