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Question Number 121222 by benjo_mathlover last updated on 06/Nov/20

$$\underset{x\to -\mathrm{\infty }}{\lim }\frac{\sqrt{1+{\mathrm{x}}^2}-\mathrm{x}+1}{\mathrm{x}+1}?$$

Answered by liberty last updated on 06/Nov/20

$$\underset{x\to -\mathrm{\infty }}{\lim }\frac{\mid \mathrm{x}\mid \sqrt{1+\frac{1}{{\mathrm{x}}^2}}-\mathrm{x}(1-\frac{1}{\mathrm{x}})}{\mathrm{x}(1+\frac{1}{\mathrm{x}})}=$$$$\underset{x\to -\mathrm{\infty }}{\lim }\frac{-\mathrm{x}(\sqrt{1+\frac{1}{{\mathrm{x}}^2}}+(1-\frac{1}{\mathrm{x}}))}{\mathrm{x}(1+\frac{1}{\mathrm{x}})}=-2.$$

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