Question Number 131654 by mohammad17 last updated on 07/Feb/21 $$\underset{\mathrm{0}} {\int}^{\:\mathrm{1}/\mathrm{64}} \frac{{tan}^{−\mathrm{1}} {x}}{\:\sqrt{{x}}}{dx} \\ $$ Answered by mathmax by abdo last updated on 07/Feb/21 $$\mathrm{I}=\int_{\mathrm{0}}…
Question Number 581 by 123456 last updated on 31/Jan/15 $${z}^{\mathrm{2}} =\mathrm{cos}\:\theta+{i}\mathrm{sin}\:\theta \\ $$$${z}=? \\ $$ Answered by ssahoo last updated on 31/Jan/15 $${e}^{{i}\theta} =\mathrm{cos}\:\theta\:+{i}\mathrm{sin}\:\theta={z}^{\mathrm{2}} \\…
Question Number 66098 by aliesam last updated on 09/Aug/19 Commented by Prithwish sen last updated on 09/Aug/19 $$\left(\mathrm{cosx}+\boldsymbol{\mathrm{i}}\mathrm{sinx}\right)^{\mathrm{5}} =\mathrm{cos5x}+\boldsymbol{\mathrm{i}}\mathrm{sin5x}\:=\:\mathrm{cos}^{\mathrm{5}} \mathrm{x}+\mathrm{5}\boldsymbol{\mathrm{i}}\mathrm{cos}^{\mathrm{4}} \mathrm{xsinx}−\mathrm{10cos}^{\mathrm{3}} \mathrm{xsin}^{\mathrm{2}} \mathrm{x}−\mathrm{10}\boldsymbol{\mathrm{i}}\mathrm{cos}^{\mathrm{2}} \mathrm{xsin}^{\mathrm{3}} \mathrm{x}+\mathrm{5cosxsin}^{\mathrm{4}}…
Question Number 560 by 123456 last updated on 26/Jan/15 $${u}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${v}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$$\begin{cases}{{u}\left({x}\right){v}\left({x}\right)={x}^{\mathrm{2}} −{v}\left(−{x}\right)}\\{{u}\left(−{x}\right){v}\left({x}\right)={x}^{\mathrm{3}} +{v}\left(−{x}\right)}\end{cases} \\ $$$${h}\left({x}\right)={u}\left({x}\right){v}\left({x}\right)=? \\ $$ Answered by prakash jain last…
Question Number 131620 by mohammad17 last updated on 06/Feb/21 Answered by Dwaipayan Shikari last updated on 06/Feb/21 $$\underset{{z}\rightarrow\mathrm{2}{e}^{\frac{{i}\pi}{\mathrm{3}}} } {\mathrm{lim}}\frac{{z}^{\mathrm{3}} +\mathrm{8}}{{z}^{\mathrm{4}} +\mathrm{4}{z}^{\mathrm{2}} +\mathrm{16}}=\underset{{z}\rightarrow\mathrm{2}{e}^{\frac{{i}\pi}{\mathrm{3}}} } {\mathrm{lim}}\frac{{z}+\mathrm{2}}{{z}^{\mathrm{2}}…
Question Number 131622 by rydasss last updated on 06/Feb/21 $${for}\:-\pi\:<\:{x}\:<\:-\:\frac{\pi}{\mathrm{2}}\:{find}\:{the}\:{solution}\:{of} \\ $$$${sin}\:{x}\:>\:\:\frac{{sin}\:{x}\:+\:\mathrm{2}}{\mathrm{2}\:{sin}\:{x}\:+\:\mathrm{1}} \\ $$ Answered by mr W last updated on 07/Feb/21 $$−\pi<{x}<−\frac{\pi}{\mathrm{2}}\:\Rightarrow\:−\mathrm{1}<\mathrm{sin}\:{x}<\mathrm{0} \\ $$$${case}\:\mathrm{1}:\:\mathrm{2sin}\:{x}+\mathrm{1}>\mathrm{0},\:{i}.{e}.\:\mathrm{sin}\:{x}>−\frac{\mathrm{1}}{\mathrm{2}}…
Question Number 545 by 123456 last updated on 25/Jan/15 $${if}\:\tau=\underset{\mathrm{0}} {\overset{+\infty} {\int}}{e}^{−\frac{{t}}{\mathrm{2}}} {dt}\underset{−\infty} {\overset{+\infty} {\int}}\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} },\:{then}\:\frac{\tau}{\mathrm{2}}=? \\ $$ Answered by prakash jain last updated on…
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Question Number 544 by 123456 last updated on 26/Jan/15 $$\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\int}}\mathrm{sin}\:{x}\:\mathrm{sinh}\:{x}\:{dx}=? \\ $$ Answered by prakash jain last updated on 26/Jan/15 $$\int\mathrm{sin}\:{x}\:\mathrm{sinh}\:{xdx} \\ $$$$=\mathrm{sin}\:{x}\:\mathrm{cosh}\:{x}\:−\int\mathrm{cos}\:{x}\:\mathrm{cosh}\:{x}\:{dx}…
Question Number 543 by 123456 last updated on 25/Jan/15 $${if}\:{f}'\left({x}\right)={f}\left({x}\right)+{x},\:{f}\left(\mathrm{0}\right)=\mathrm{0},\:{then} \\ $$$${f}\left(\mathrm{1}\right)=? \\ $$ Answered by prakash jain last updated on 24/Jan/15 $${y}={f}\left({x}\right) \\ $$$${y}'−{y}={x}…