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Question Number 78791 by jagoll last updated on 20/Jan/20

$$$$$$$$$$\underset{x\to \mathrm{\infty }}{\lim }\sqrt{2+3\mathrm{x}-{\mathrm{x}}^2}-\sqrt{{\mathrm{x}}^2-2\mathrm{x}+2}?$$

Answered by john santu last updated on 20/Jan/20

$$\underset{x\to \mathrm{\infty }}{\lim }\sqrt{x^2(\frac{2}{x^2}+\frac{3}{x}-1)}-\sqrt{x^2(1-\frac{2}{x}+\frac{2}{x^2})}=$$$$\underset{x\to \mathrm{\infty }}{\lim }\mid x\mid \sqrt{\frac{2}{x^2}+\frac{3}{x}-1}-\mid x\mid \sqrt{1-\frac{2}{x}+\frac{2}{x^2}}=$$$$\underset{x\to \mathrm{\infty }}{\lim }\mid x\mid \left(i\right)-\mid x\mid \left(1\right)=\mathrm{\infty }$$

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