Question Number 174915 by cortano1 last updated on 14/Aug/22 $$\:{Find}\:{the}\:{value}\:{of}\:{a}\:{for}\:{which}\: \\ $$$$\:{the}\:{limit}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left({ax}\right)−\mathrm{arctan}\:{x}−{x}}{{x}^{\mathrm{3}} +{x}^{\mathrm{4}} } \\ $$$${is}\:{finite}\:{and}\:{then}\:{evaluate}\:{the}\:{limit} \\ $$ Answered by Ar Brandon last updated…
Question Number 174883 by infinityaction last updated on 13/Aug/22 $$\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\mathrm{1}} {e}^{{x}^{\mathrm{2}} } \mathrm{sin}\left({nx}\right){dx}\: \\ $$ Answered by Mathspace last updated on 14/Aug/22 $${u}_{{n}}…
Question Number 174876 by infinityaction last updated on 13/Aug/22 $$\:\:\mathrm{let}\:{f}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R}\:{be}\:{a}\:\mathrm{continuous} \\ $$$$\:\mathrm{function}\:\mathrm{ditermine}\:\left(\mathrm{with}\:\mathrm{appropriate}\right. \\ $$$$\left.\mathrm{justification}\right)\:\mathrm{the}\:\mathrm{following}\: \\ $$$$\:\:\mathrm{limit}:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\mathrm{1}} {nx}^{{n}} {f}\left({x}\right){dx} \\ $$ Answered by TheHoneyCat…
Question Number 174863 by cortano1 last updated on 13/Aug/22 Commented by kaivan.ahmadi last updated on 13/Aug/22 $${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{\mathrm{1}−\left(\mathrm{1}+\frac{{x}^{\mathrm{4}} }{\mathrm{2}}\right)\left(\mathrm{1}−\frac{{x}^{\mathrm{4}} }{\mathrm{2}}\right)}{{x}^{\mathrm{8}} }= \\ $$$${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{\mathrm{1}−\left(\mathrm{1}−\frac{{x}^{\mathrm{8}} }{\mathrm{4}}\right)}{{x}^{\mathrm{8}}…
Question Number 174841 by infinityaction last updated on 12/Aug/22 $$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}\mathrm{sin}\left(\mathrm{sin}{x}\right)−\mathrm{sin}^{\mathrm{2}} {x}\:\:}{{x}^{\mathrm{6}} } \\ $$ Answered by Ar Brandon last updated on 12/Aug/22 $$\mathcal{A}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}\mathrm{sin}\left(\mathrm{sin}{x}\right)−\mathrm{sin}^{\mathrm{2}}…
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 $$ \\…