Haiurre lim _(xarrow infty )(x^p)/(e^x) no npassiny Jonwrana H OObACHHTE nonyqenHoe cpaBHeHKC : GecKOHe9HO 60JIbIIIHX.

To evaluate the limit $\lim_{x\to\infty}\frac{x^p}{e^x}$, we can use L'Hôpital's Rule. Taking the derivative of the numerator and denominator, we get:<br /><br />$\lim_{x\to\infty}\frac{p x^{p-1}}{e^x}$<br /><br />Applying L'Hôpital's Rule again, we get:<br /><br />$\lim_{x\to\infty}\frac{p(p-1) x^{p-2}}{e^x}$<br /><br />Continuing this process, we eventually get:<br /><br />$\lim_{x\to\infty}\frac{p!}{e^x}$<br /><br />Since the denominator grows exponentially while the numerator is a constant, the limit is 0.