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 184883 by mathlove last updated on 13/Jan/23

$$\underset{x\to 2}{\lim }\frac{\sqrt{x-2}}{x-2}=?$$

Answered by aba last updated on 13/Jan/23

$$\underset{x\to 2}{\lim }\frac{\sqrt{\mathrm{x}-2}}{\mathrm{x}-2}=\underset{x\to 2^{+}}{\lim }\frac{1}{\sqrt{\mathrm{x}-2}}=\frac{1}{0^{+}}=+\mathrm{\infty }$$

Commented by Frix last updated on 13/Jan/23

$$\underset{x\to 2}{\lim }f\left(x\right)\mathrm{is}\mathrm{not}\mathrm{the}\mathrm{same}\mathrm{as}\underset{x\to 2^{+}}{\lim }f\left(x\right)\mathrm{if}$$$$\underset{x\to 2^{-}}{\lim }f\left(x\right){\mathrm{doesn}}^{\prime }\mathrm{t}\mathrm{exist}.$$$$\underset{x\to 2}{\lim }f\left(x\right){\mathrm{doesn}}^{\prime }\mathrm{t}\mathrm{exist}\mathrm{if}\underset{x\to 2^{-}}{\lim }f\left(x\right)\ne \underset{x\to 2^{+}}{\lim }f\left(x\right)$$

Commented by aba last updated on 13/Jan/23

$$\mathrm{the}\mathrm{function}\mathrm{is}\mathrm{undefined}\mathrm{on}\mathrm{the}\mathrm{left}\mathrm{side}$$

Commented by Frix last updated on 13/Jan/23

$$\mathrm{Yes}.\mathrm{This}\mathrm{means},\mathrm{the}\mathrm{limit}{\mathrm{doesn}}^{\prime }\mathrm{t}\mathrm{exist}.$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com