Question

lim x^2*e^-10x
x->+оо
помогите решить предел номер 7.8

Answer 1

$displaystyle lim_{x to+ infty} x^2e^{-10x}=lim_{x to+ infty} frac{x^2}{e^{10x}} =bigg{ frac{infty}{infty}bigg}=lim_{x to+ infty} frac{(x^2)'}{(e^{10x})'} =\ \ \ =lim_{x to+ infty} frac{2x}{10e^{10x}} = frac{1}{5} lim_{x to+ infty} frac{(x)'}{(e^{10x})'} = frac{1}{50} lim_{x to+ infty} frac{1}{e^{10x}} =0$