Question

limx→−∞ xe^x

Answer 1

\[\lim_{x \rightarrow -\infty} xe ^{x}\]

Answer 2

\[\lim_{x\to-\infty}xe^x=\lim_{x\to-\infty}\frac{x}{e^{-x}}=\frac{-\infty}{\infty}\]
Apply L'Hopital's rule:
\[\lim_{x\to-\infty}\frac{x}{e^{-x}}=\lim_{x\to-\infty}\frac{1}{-e^{-x}}=\lim_{x\to-\infty}-e^x=\cdots\]