Question and Answers Forum

All Questions      Topic List

Limits Questions

Previous in All Question      Next in All Question      

Previous in Limits      Next in Limits      

Question Number 75929 by Rio Michael last updated on 21/Dec/19

$$Evaluate$$$$\underset{x\to -\mathrm{\infty }}{\lim }\left[\sqrt{1-{xe}^x}\right]$$

Commented by kaivan.ahmadi last updated on 21/Dec/19

$${lim}_{x\to -\mathrm{\infty }}{xe}^x={lim}_{x\to -\mathrm{\infty }}\frac{x}{e^{-x}}={lim}_{x\to -\mathrm{\infty }}\frac{1}{-e^{-x}}=0^{-}$$$$\Rightarrow {lim}_{x\to -\mathrm{\infty }}\sqrt{1-{xe}^x}=\sqrt{1-0^{-}}=\sqrt{1^{+}}=1^{+}$$$$\Rightarrow {lim}_{x\to -\mathrm{\infty }}\left[\sqrt{1-{xe}^x}\right]=\left[1^{+}\right]=1$$

Commented by Rio Michael last updated on 21/Dec/19

$$thankssir$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com