Question

limita din e^x(x^2+4x+1) cand x tinde la -infinit/ infinit.
Mulțumesc!

Answer 1

$\lim\limits_{x\to+ \infty}\Big[e^x(x^2+4x+1)\Big] = \infty\cdot \infty = \infty \\ \\ \lim\limits_{x\to-\infty}\Big[e^x(x^2+4x+1)\Big] = \lim\limits_{x\to-\infty}\dfrac{(x^2+4x+1)}{e^{-x}} = \lim\limits_{x\to-\infty}\dfrac{(2x+4)}{-e^{-x}} = \\ \\ = \lim\limits_{x\to-\infty}\dfrac{2}{e^{-x}} =0$