Weird limit with $e^x$

HINT

Let $y=-x\to \infty$, then

$$\lim\limits_{x\to -\infty} [(x^2+1)e^x]=\lim\limits_{y\to \infty} [(y^2+1)e^{-y}]=\lim\limits_{y\to \infty} \frac{y^2+1}{e^{y}}$$

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Limits

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