Question Number 43754 by Meritguide1234 last updated on 15/Sep/18 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 109284 by bobhans last updated on 22/Aug/20 Answered by abdomsup last updated on 22/Aug/20 $${f}\left({x}\right)=\frac{\sqrt{\pi−\mathrm{2}{x}}−\sqrt{\pi+\mathrm{4}{x}}}{{cos}\left({x}−\frac{\pi}{\mathrm{2}}\right)} \\ $$$${we}\:{have}\:{f}\left({x}\right)=\frac{\sqrt{\pi−\mathrm{2}{x}}−\sqrt{\pi+\mathrm{4}{x}}}{{sinx}} \\ $$$$\sqrt{\pi−\mathrm{2}{x}}=\sqrt{\pi}\sqrt{\mathrm{1}−\frac{\mathrm{2}{x}}{\pi}}\sim\sqrt{\pi}\left(\mathrm{1}−\frac{{x}}{\pi}\right) \\ $$$$\sqrt{\pi+\mathrm{4}{x}}=\sqrt{\pi}\sqrt{\mathrm{1}+\frac{\mathrm{4}{x}}{\pi}}\sim\sqrt{\pi}\left(\mathrm{1}+\frac{\mathrm{2}{x}}{\pi}\right) \\ $$$${sinx}\:\sim{x}\:\Rightarrow…
Question Number 43679 by gunawan last updated on 14/Sep/18 $$\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{i}^{\mathrm{2}} }{\mathrm{2}^{{i}} \:}=… \\ $$ Commented by abdo.msup.com last updated on 14/Sep/18 $${let}\:{p}\left({x}\right)=\sum_{{k}=\mathrm{0}} ^{\infty}…
Question Number 174715 by infinityaction last updated on 09/Aug/22 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}cos}\left(\frac{\pi}{\mathrm{4}}\right)\mathrm{cos}\left(\frac{\pi}{\mathrm{8}}\right)\:…\:\mathrm{cos}\left(\frac{\pi}{\mathrm{2}^{{n}+\mathrm{1}} }\right)\: \\ $$ Answered by abdullahoudou last updated on 09/Aug/22 $$\mathrm{cos}\:\left(\frac{\pi}{\mathrm{2}^{{n}} }\right)=\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}^{{n}−\mathrm{1}} }\right)\frac{\mathrm{1}}{\mathrm{2sin}\:\left(\pi/\mathrm{2}^{{n}} \right)}…
Question Number 174683 by infinityaction last updated on 08/Aug/22 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left[\frac{{x}^{\mathrm{2}} }{\mathrm{sin}{x}\:\mathrm{tan}{x}\:}\right] \\ $$$$\left[\centerdot\right]\:{greatest}\:{integer}\:{function} \\ $$ Answered by a.lgnaoui last updated on 09/Aug/22 $$ \\…
Question Number 109139 by bemath last updated on 21/Aug/20 $$\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\left(\mathrm{1}−{x}\right)\:\mathrm{sin}\:\mid\mathrm{2}{x}−\mathrm{2}\mid\:? \\ $$ Commented by kaivan.ahmadi last updated on 21/Aug/20 $${x}\rightarrow−\infty\Rightarrow\mathrm{2}{x}−\mathrm{2}\rightarrow−\infty\Rightarrow\mid\mathrm{2}{x}−\mathrm{2}\mid\rightarrow+\infty\Rightarrow \\ $$$$−\mathrm{1}\leqslant{sin}\mid\mathrm{2}{x}−\mathrm{2}\mid\leqslant\mathrm{1}\:{is}\:{an}\:{element}\:{of}\:{R}\:{we} \\ $$$${say}\:{a}.…
Question Number 174630 by infinityaction last updated on 06/Aug/22 $$\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{r}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{r}}{{n}^{\mathrm{2}} +{r}} \\ $$ Answered by mnjuly1970 last updated on 06/Aug/22 $$\:\:\:\:\:{lim}_{{n}\rightarrow\infty} \left\{\frac{\mathrm{1}}{\mathrm{1}+{n}^{\:\mathrm{2}}…
Question Number 109091 by bemath last updated on 21/Aug/20 $$\:\:\:\:\frac{\bigtriangleup\flat{e}\mathscr{M}{ath}\bigtriangledown}{\equiv\multimap\equiv\multimap\equiv} \\ $$$$\:\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}}{\:\sqrt{\pi+\mathrm{tan}\:{x}}−\sqrt{\pi−\mathrm{tan}\:{x}}}\:? \\ $$ Answered by bobhans last updated on 21/Aug/20 Commented by bobhans…
Question Number 109068 by n0y0n last updated on 20/Aug/20 Answered by Dwaipayan Shikari last updated on 20/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left({cos}\mathrm{5}{x}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{{x}^{\mathrm{4}} }} =\left(\mathrm{1}−\frac{\mathrm{25}{x}^{\mathrm{4}} }{\mathrm{2}}\right)^{\frac{−\mathrm{2}}{{x}^{\mathrm{4}} .\mathrm{25}}.\left(\frac{−\mathrm{25}}{\mathrm{2}}\right)} ={e}^{−\frac{\mathrm{25}}{\mathrm{2}}}…
Question Number 109067 by n0y0n last updated on 20/Aug/20 Answered by Aziztisffola last updated on 20/Aug/20 $$\:\mathrm{sin}\left(\mathrm{x}\right)\mathrm{ln}\left(\mathrm{cot}^{\mathrm{2}} \left(\mathrm{x}\right)\right)=\mathrm{sin}\left(\mathrm{x}\right)\mathrm{ln}\left(\frac{\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}\right)}{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right)}\right) \\ $$$$\:=\mathrm{sin}\left(\mathrm{x}\right)\left(\mathrm{ln}\left(\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}\right)\right)−\mathrm{sin}\left(\mathrm{x}\right)\mathrm{ln}\left(\mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right)\right)\right. \\…