Question Number 90432 by jagoll last updated on 23/Apr/20
![lim_(x→−∞) x[(√(x^2 +1))−x ] =?](Q90432.png)
$$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\mathrm{x}\left[\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}−\mathrm{x}\:\right]\:=? \\ $$
Commented by mathmax by abdo last updated on 23/Apr/20
$${we}\:{have}\:{lim}_{{x}\rightarrow−\infty} \:{x}\:=−\infty\:\:{and} \\ $$$${lim}_{{x}\rightarrow−\infty} \sqrt{{x}^{\mathrm{2}} +\mathrm{1}}−{x}\:=+\infty\:\Rightarrow{lim}_{{x}\rightarrow−\infty} {x}\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}−{x}\right)\:=−\infty \\ $$
Answered by jagoll last updated on 23/Apr/20
