Category: Limits

Question Number 190824 by cortano12 last updated on 12/Apr/23 $$\underset{x\to \frac{\pi }{4}}{\lim }\frac{\sec {}^2\mathrm{x}-2\sqrt{\tan \mathrm{x}}}{2\cos \mathrm{x}-2\sin \mathrm{x}}=?$$ Commented by 0670322918 last updated on 12/Apr/23 $$\frac{\mathrm{1}}{\mathrm{2}}\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\frac{{tan}^{\mathrm{2}} \left({x}\right)+\mathrm{1}−\mathrm{2}+\mathrm{2}−\mathrm{2}\sqrt{{tan}\left({x}\right)}}{{cos}\left({x}\right)\left[\mathrm{1}−{tan}\left({x}\right)\right]}= \…

Question Number 125282 by Mammadli last updated on 09/Dec/20 $$1.\underset{\mathit{n}=1}{\sum ^{\mathrm{\infty }}}\sqrt[\mathit{n}]{\frac{2\mathit{n}-1}{2\mathit{n}+1}}=?$$$$2.\underset{\mathit{n}\to \mathrm{\infty }}{\mathit{l}\mathit{i}\mathit{m}}\sqrt[\mathit{n}]{\frac{2\mathit{n}-1}{2\mathit{n}+1}}=?$$ Answered by mathmax by abdo last updated on…

Question Number 59694 by meme last updated on 13/May/19 $$li\underset{x\to 0}{m}\frac{cos(\sqrt{\mid x\mid )-1}}{x}=?$$ Commented by maxmathsup by imad last updated on 13/May/19 $${let}\:{A}\left({x}\right)\:=\frac{{cos}\left(\sqrt{\mid{x}\mid}\right)−\mathrm{1}}{{x}}\:\:\:\:{we}\:{have}\:{cos}\left({u}\right)\:\sim\mathrm{1}−\frac{{u}^{\mathrm{2}} }{\mathrm{2}}\:\left(\:\:{u}\in{V}\left(\mathrm{0}\right)\right)\:\Rightarrow \…

Question Number 59637 by mathtype last updated on 12/May/19 $$\underset{x\to \mathrm{\infty }}{lim}\frac{1}{x}{\int }_0^x\mid \sin x\mid$$ Commented by Mr X pcx last updated on 13/May/19 $${there}\:{is}\:{a}\:{problem}\:{here}\:{let}\:{take}\:{x}={n}\pi…

Question Number 59599 by tanmay last updated on 12/May/19 Answered by tanmay last updated on 12/May/19 $$T_r=\frac{tan\frac{x}{2^{r+1}}(1+{tan}^2\frac{x}{2^{r+1}})}{1-{tan}^2\frac{x}{2^{r+1}}}$$$${T}_{{r}}…