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 128624 by john_santu last updated on 09/Jan/21

$$\underset{x\to 0}{\lim }\frac{\mid {\mathrm{x}}^2+1\mid -\mid {\mathrm{x}}^2-1\mid }{\mid 2000\mathrm{x}+5\mid -\mid 2000\mathrm{x}-5\mid }=?$$

Answered by liberty last updated on 09/Jan/21

$$\underset{x\to 0}{\lim }\frac{({\mathrm{x}}^2+1)+({\mathrm{x}}^2-1)}{(2000\mathrm{x}+5)+(2000\mathrm{x}-5)}=\underset{x\to 0}{\lim }\frac{{2\mathrm{x}}^2}{4000\mathrm{x}}=0$$

Answered by mathmax by abdo last updated on 09/Jan/21

$${\lim }_{\mathrm{x}\to 0_{+}}\mathrm{f}\left(\mathrm{x}\right)={\lim }_{\mathrm{x}\to 0^{+}}\frac{{\mathrm{x}}^2+1-(1-{\mathrm{x}}^2)}{2000\mathrm{x}+5-2000\mathrm{x}+5}={\lim }_{\mathrm{x}\to 0^{+}}\frac{{2\mathrm{x}}^2}{10}=0$$$${\lim }_{\mathrm{x}\to 0^{-}}\mathrm{f}\left(\mathrm{x}\right)={\lim }_{\mathrm{x}\to 0^{-}}\frac{{\mathrm{x}}^2+1-(1-{\mathrm{x}}^2)}{5-2000\mathrm{x}-(2000\mathrm{x}+5)}={\lim }_{\mathrm{x}\to 0^{-}}\frac{{2\mathrm{x}}^2}{-4000\mathrm{x}}$$$$=-{\lim }_{\mathrm{x}\to 0^{-}}\frac{\mathrm{x}}{2000}=0$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com