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 69593 by ahmadshahhimat775@gmail.com last updated on 25/Sep/19

Commented by mathmax by abdo last updated on 25/Sep/19

$$letf\left(x\right)=\frac{\sqrt{6-x}-2}{3-\sqrt{11-x}}\Rightarrow$$$${lim}_{x\to 2}f\left(x\right)={lim}_{x\to 2}\frac{(\sqrt{6-x}-2)(\sqrt{6-x}+2)(3+\sqrt{11-x})}{(3-\sqrt{11-x})(3+\sqrt{11-x})(\sqrt{6-x}+2)}$$$$={lim}_{x\to 2}\frac{(6-x-4)(3+\sqrt{11-x})}{(9-11+x)(\sqrt{6-x}+2)}$$$$={lim}_{x\to 2}\frac{(2-x)(3+\sqrt{11-x})}{(x-2)(\sqrt{6-x}+2)}$$$$={lim}_{x\to 2}-\frac{3+\sqrt{11-x}}{2+\sqrt{6-x}}=-\frac{3+3}{2+2}=-\frac{6}{4}=-\frac{3}{2}$$

Commented by Rasheed.Sindhi last updated on 26/Sep/19

$$Vnice!$$

Answered by MJS last updated on 25/Sep/19

$$\underset{x\to 2}{\lim }\frac{\sqrt{6-x}-2}{3-\sqrt{11-x}}=\underset{x\to 2}{\lim }\frac{\frac{d}{dx}[\sqrt{6-x}-2]}{\frac{d}{dx}[3-\sqrt{11-x}]}=$$$$=-\underset{x\to 2}{\lim }\frac{\sqrt{11-x}}{\sqrt{6-x}}=-\frac{3}{2}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com