Question Number 65052 by AnjanDey last updated on 24/Jul/19 $${A}.\mathrm{Evaluate}: \\ $$$$\left(\mathrm{i}\right)\int\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{9}+\mathrm{16sin}\:\mathrm{2}{x}}{dx} \\ $$$$\left(\mathrm{ii}\right)\int\frac{\mathrm{1}+{x}^{\mathrm{2}} }{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)\sqrt{\mathrm{1}+{x}^{\mathrm{2}} +{x}^{\mathrm{4}} }}{dx} \\ $$$$\left(\mathrm{iii}\right)\int\frac{{x}−\mathrm{1}}{\left({x}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{3}} +{x}+{x}^{\mathrm{2}} }}{dx} \\ $$ Answered…
Question Number 130555 by Dwaipayan Shikari last updated on 26/Jan/21 $$\frac{\mathrm{1}}{\left(\mathrm{2}−\pi\right)^{\mathrm{2}} }+\frac{\mathrm{1}}{\left(\mathrm{2}+\pi\right)^{\mathrm{2}} }+\frac{\mathrm{1}}{\left(\mathrm{6}−\pi\right)^{\mathrm{2}} }+\frac{\mathrm{1}}{\left(\mathrm{6}+\pi\right)^{\mathrm{2}} }+\frac{\mathrm{1}}{\left(\mathrm{10}−\pi\right)^{\mathrm{2}} }+\frac{\mathrm{1}}{\left(\mathrm{10}+\pi\right)^{\mathrm{2}} }+..=\frac{\pi^{\mathrm{2}} }{\mathrm{16}}{sec}^{\mathrm{2}} \left(\frac{\pi^{\mathrm{2}} }{\mathrm{4}}\right) \\ $$$${Prove}\:{or}\:{disprove} \\ $$ Answered…
Question Number 65013 by Rio Michael last updated on 24/Jul/19 $${why}\:{do}\:{we}\:{divide}\:{each}\:{term}\:{by}\:{n}\:{when}\:{given}\:{the}\:{question} \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{3}\:+\mathrm{2}{n}}{\mathrm{1}+{n}}\:? \\ $$ Answered by Tanmay chaudhury last updated on 24/Jul/19 $$\underset{{n}\rightarrow\infty}…
Question Number 65011 by AnjanDey last updated on 24/Jul/19 $$\mathrm{1}.\left(\mathrm{i}\right)\mathrm{Evaluate}:\int\frac{\mathrm{1}}{\mathrm{sin}\:{x}−\mathrm{cos}\:{x}+\sqrt{\mathrm{2}}}{dx} \\ $$$$\left(\mathrm{ii}\right)\mathrm{Evaluate}:\int\mathrm{2}^{\mathrm{2}^{\mathrm{2}^{{x}} } } \mathrm{2}^{\mathrm{2}^{{x}} } \mathrm{2}^{{x}} \:{dx} \\ $$$$\left(\mathrm{iii}\right)\mathrm{Evaluate}:\int\frac{\mathrm{cos}\:^{\mathrm{3}} {x}}{\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{sin}\:{x}}{dx} \\ $$$$\mathrm{2}.\mathrm{cosec}\:\left[\mathrm{tan}^{−\mathrm{1}} \left\{\mathrm{cos}\:\left(\mathrm{cot}^{−\mathrm{1}}…
Question Number 130549 by EDWIN88 last updated on 26/Jan/21 $${the}\:{solution}\:{of}\:{equation}\: \\ $$$$\mid{z}\mid−{z}\:=\:\mathrm{1}+\mathrm{2}{i}\:{is}\:\_\_ \\ $$ Answered by Dwaipayan Shikari last updated on 26/Jan/21 $${z}={x}+{iy} \\ $$$$\sqrt{{x}^{\mathrm{2}}…
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Question Number 130449 by Dwaipayan Shikari last updated on 25/Jan/21 $$\frac{\mathrm{1}}{\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }−\frac{\mathrm{1}}{\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }+\frac{\mathrm{1}}{\left(\mathrm{6}−\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }−\frac{\mathrm{1}}{\left(\mathrm{6}+\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }+\frac{\mathrm{1}}{\left(\mathrm{10}−\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }−\frac{\mathrm{1}}{\left(\mathrm{10}+\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }+.. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 130415 by Dwaipayan Shikari last updated on 25/Jan/21 $$\frac{\pi}{{e}}{sin}\left(\mathrm{1}\right)−\frac{\pi^{\mathrm{2}} }{\mathrm{2}{e}^{\mathrm{2}} }{sin}\left(\mathrm{2}\right)+\frac{\pi^{\mathrm{3}} }{\mathrm{3}{e}^{\mathrm{3}} }{sin}\left(\mathrm{3}\right)−\frac{\pi^{\mathrm{4}} }{\mathrm{4}{e}^{\mathrm{4}} }{sin}\left(\mathrm{4}\right)+… \\ $$ Commented by Dwaipayan Shikari last updated…
Question Number 64872 by Rio Michael last updated on 22/Jul/19 $${Given}\:{that}\: \\ $$$$\:{y}\:=\:\left({cosx}^{} \right)^{{sinx}} \:\:{find}\:\frac{{dy}}{{dx}} \\ $$$${and}\: \\ $$$$\:\:\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:{y} \\ $$ Commented by kaivan.ahmadi…
Question Number 64871 by Rio Michael last updated on 22/Jul/19 $${any}\:{hint}\:{about}\:{how}\:{to}\:{prove}\:{by}\:{induction}\:{in}\:{the}\:{Sigma}\:{notion}\:{topic}? \\ $$$${like}\:{in}\:\Sigma \\ $$ Commented by mathmax by abdo last updated on 22/Jul/19 $${you}\:{question}\:{is}\:{not}\:{clear}….…