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Question Number 121576 by oustmuchiya@gmail.com last updated on 09/Nov/20

Answered by TANMAY PANACEA last updated on 09/Nov/20

$$f\left(x\right)=\frac{(\sqrt{x^2+15}-5)(\sqrt{x^2+15}+5)}{(x-2)(\sqrt{x^2+15}+5)}$$$$=\frac{x^2+15-25}{(x-2)(\sqrt{x^2+15}+5)}=\frac{x^2-10}{(x-2)(\sqrt{x^2+15}+5)}$$$$atx=2thefunction[discontinous$$$$li\underset{x\to 2}{mf}\left(x\right)=\mathrm{\infty }$$$$$$

Answered by TANMAY PANACEA last updated on 09/Nov/20

$$f\left(x\right)=\frac{x\sqrt{1+\frac{15}{x^2}}-5}{x-2}=\frac{\sqrt{1+\frac{15}{x^2}}-\frac{5}{x}}{1-\frac{2}{x}}$$$$soli\underset{x\to \mathrm{\infty }}{m}f\left(x\right)$$$$=\frac{\sqrt{1+0}-0}{1-0}=1$$

Commented by oustmuchiya@gmail.com last updated on 12/Nov/20

$$\mathrm{many}\mathrm{thanks}\mathrm{indeed}$$

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