Category: Limits

Question Number 195066 by alcohol last updated on 23/Jul/23 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 195033 by mathlove last updated on 22/Jul/23 $$anypointisthefunctionis$$$$notcontinous$$$$f\left(x\right)={(4x+8)}^{\frac{ln45}{8}}$$$$a)-8b)-2$$$$c)nooned)5$$ Answered by alephzero last updated…

Question Number 195021 by tri26112004 last updated on 22/Jul/23 $$\underset{x\to 0}{\lim }\frac{x-sinx}{x^n}=¿(n\in N^{\ast })$$ Answered by MM42 last updated on 22/Jul/23 $$ifx\to 0\Rightarrow x-sinx\sim \frac{1}{6}{x}^3$$$$\Rightarrow{if}\:\:\:{n}<\mathrm{3}\:\Rightarrow\:{lim}=\mathrm{0}…

Question Number 194968 by cortano12 last updated on 21/Jul/23 Answered by tri26112004 last updated on 21/Jul/23 $$=\underset{x\to 0}{\lim }\frac{1}{\sqrt{x+1}+\sqrt{1-x}}.-\underset{x\to 0}{\lim }\frac{\sqrt{x+1}+\sqrt{1-x}-2}{x^2}$$$$=−\frac{\mathrm{1}}{\mathrm{2}}.\left\{\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{1}}{\mathrm{2}}\left[\sqrt{\mathrm{4}{x}+\mathrm{4}}−\left({x}+\mathrm{2}\right)\right]+\sqrt{\mathrm{1}−{x}}+\frac{\mathrm{1}}{\mathrm{2}}{x}−\mathrm{1}}{{x}^{\mathrm{2}} }\right\} \…

Question Number 194879 by tri26112004 last updated on 18/Jul/23 Answered by cortano12 last updated on 18/Jul/23 $$=\underset{u\to 0}{\lim }\frac{{(1+2u)}^u-1}{{(1+3u)}^u-1}$$$$[u=\frac{1}{x}]$$$$\:{then}\:{apply}\:{L}'{Hopital}\: \…