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Question Number 73017 by Rio Michael last updated on 05/Nov/19

find    lim_(x→+∞)   x(√(x^2  + 1))

$${find}\: \\ $$$$\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:\:{x}\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{1}}\: \\ $$

Commented by mathmax by abdo last updated on 05/Nov/19

=lim_(x→+∞) x(√(x^2 (1+(1/x^2 ))))=lim_(x→+∞) x^2 (√(1+(1/x^2 )))=lim_(x→+∞) x^2 =+∞

$$\left.={lim}_{{x}\rightarrow+\infty} {x}\sqrt{{x}^{\mathrm{2}} \left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right.}\right)={lim}_{{x}\rightarrow+\infty} {x}^{\mathrm{2}} \sqrt{\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }}={lim}_{{x}\rightarrow+\infty} {x}^{\mathrm{2}} =+\infty \\ $$

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