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 27701 by NECx last updated on 13/Jan/18

$$Ifthefunctionf\left(x\right)satisfies$$$$\underset{x\to 1}{\lim }\frac{f\left(x\right)-2}{x^2-1}=\pi ,evaluate\underset{x\to 1}{\lim }f\left(x\right)$$

Commented by abdo imad last updated on 21/Jan/18

$$\iff {lim}_{x\to 1}\frac{f\left(x\right)-2-\pi (x^2-1)}{x^2-1}=0sowemusthave$$$${lim}_{x\to 1}f\left(x\right)-2-\pi (x^2-1)=0inordertofindtheform\frac{0}{0}$$$$\Rightarrow {lim}_{x\to 1}f\left(x\right)=2letverifythisnumberbyhospital$$$$theorem{lim}_{x\to 1}\frac{f^{{}^{\prime }}\left(x\right)-2\pi x}{2x}=0\Rightarrow {lim}_{x\to 1}{f}^{{}^{\prime }}\left(x\right)=2\pi so$$$$wemusthave{lim}_{x\to 1}f\left(x\right)=2and{lim}_{x\to 1}{f}^{{}^{\prime }}\left(x\right)=2\pi .$$

Answered by mrW2 last updated on 13/Jan/18

$$\underset{x\to 1}{\lim }f\left(x\right)=2$$

Commented by NECx last updated on 13/Jan/18

$$how?$$

Commented by mrW2 last updated on 14/Jan/18

$$if\underset{x\to 1}{\lim }f\left(x\right)\ne 2,$$$$\underset{x\to 1}{\lim }\frac{f\left(x\right)-2}{x^2-1}=\frac{finite}{0}\to \mathrm{\infty }\ne \pi$$

Commented by abdo imad last updated on 21/Jan/18

$$thisconditionisunsufficient....$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com