Question and Answers Forum

All Questions      Topic List

Limits Questions

Previous in All Question      Next in All Question      

Previous in Limits      Next in Limits      

Question Number 134173 by mathlove last updated on 28/Feb/21

$$\underset{x\to 8}{\lim }\frac{\sqrt[3]{x}-2}{\sqrt{x}-2\sqrt{2}}=?$$

Answered by malwan last updated on 28/Feb/21

$$\underset{x\to 8}{lim}\frac{{}^3\sqrt{x}-2}{\sqrt{x}-2\sqrt{2}}\times \frac{{}^3\sqrt{x^2}+2{}^3\sqrt{x}+4}{{}^3\sqrt{x^2}+2{}^3\sqrt{x}+4}\times \frac{\sqrt{x}+2\sqrt{2}}{\sqrt{x}+2\sqrt{2}}$$$$=\frac{2\sqrt{2}+2\sqrt{2}}{4+4+4}=\frac{4\sqrt{2}}{4\times 3}=\frac{\sqrt{2}}{3}$$

Answered by EDWIN88 last updated on 02/Mar/21

$$\mathrm{let}\mathrm{x}={\mathrm{t}}^6\Rightarrow \underset{\mathrm{t}\to \sqrt{2}}{\lim }\left[\frac{{\mathrm{t}}^2-2}{{\mathrm{t}}^3-2\sqrt{2}}\right]=\underset{\mathrm{t}\to \sqrt{2}}{\lim }\frac{2\mathrm{t}}{{3\mathrm{t}}^2}=\frac{2}{3\times \sqrt{2}}$$$$=\frac{\sqrt{2}}{3}$$

Commented by malwan last updated on 02/Mar/21

$$\underset{t\to \sqrt{2}}{lim}\frac{t^2-2}{t^3-2\sqrt{2}}=\underset{t\to \sqrt{2}}{lim}\frac{(t-\sqrt{2})(t+\sqrt{2})}{(t-\sqrt{2})(t^2+\sqrt{2}t+2)}$$$$=\frac{\sqrt{2}+\sqrt{2}}{2+2+2}=\frac{2\times \sqrt{2}}{3\times 2}=\frac{\sqrt{2}}{3}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com