Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 165699 by lapache last updated on 06/Feb/22

$$li\underset{x\to 2}{m}\frac{x-\sqrt{x+2}}{\sqrt{4x+1}-3}=....???$$

Commented by cortano1 last updated on 07/Feb/22

$$\underset{x\to 2}{\lim }\frac{\mathrm{x}-\sqrt{\mathrm{x}+2}}{\sqrt{4\mathrm{x}+1}-3}\times \frac{\sqrt{4\mathrm{x}+1}+3}{\sqrt{4\mathrm{x}+1}+3}\times \frac{\mathrm{x}+\sqrt{\mathrm{x}+2}}{\mathrm{x}+\sqrt{\mathrm{x}+2}}$$$$=\underset{x\to 2}{\lim }\frac{\sqrt{4\mathrm{x}+1}+3}{\mathrm{x}+\sqrt{\mathrm{x}+2}}\times \underset{x\to 2}{\lim }\frac{{\mathrm{x}}^2-\mathrm{x}-2}{4\mathrm{x}-8}$$$$=\frac{6}{4}\times \underset{x\to 2}{\lim }\frac{(\mathrm{x}-2)(\mathrm{x}+1)}{4(\mathrm{x}-2)}=\frac{3}{2}\times \frac{3}{4}$$$$=\frac{9}{8}$$

Answered by nurtani last updated on 06/Feb/22

$$\underset{x\to 2}{\lim }\frac{x-\sqrt{x+2}}{\sqrt{4x+1}-3}=\underset{x\to 2}{\lim }\frac{1-\frac{1}{2\sqrt{x+2}}}{\frac{4}{2\sqrt{4x+1}}}$$$$=\frac{1-\frac{1}{2\sqrt{2+2}}}{\frac{4}{2\sqrt{4\left(2\right)+1}}}=\frac{1-\frac{1}{2\left(2\right)}}{\frac{4}{2\sqrt{9}}}=\frac{1-\frac{1}{4}}{\frac{4}{6}}=\frac{\frac{3}{4}}{\frac{2}{3}}=\frac{9}{8}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com