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If $p(x)$ is a polynomial of degree $10^{2011}$, then:

$$\lim_\limits{x \to \infty} p(x)e^{x} = ?$$

How do I even begin with this? I tried expressing it into a form where L'Hospital rule is applicable, but found that it cannot be expressed as such. Tried taking logarithm but failed there as well. So how do I find its limit. Any advice is appreciated

Natasha J
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    It is $\pm \infty$ depending on whether the highest degree term is positive or negative. – Kavi Rama Murthy Aug 05 '21 at 05:42
  • So my limit would be $+$ or $-$ $\infty$, right? But the answer given is $0$. Where am I going wrong? – Natasha J Aug 05 '21 at 05:46
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    If the answer given is 0, it sounds like there’s a missing minus sign in the exponential. Then you can L’Hopital it 10^{2011} times; the numerator gets reduced and the exp(x) in the denominator stays fixed. – evanb Aug 05 '21 at 06:09
  • Thank you @evanb. I was suspicious of the same. – Natasha J Aug 05 '21 at 06:12

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