Question Number 128808 by liberty last updated on 10/Jan/21 $$\:\mathrm{If}\:{x}\:\mathrm{cos}\:{q}\:−\:\mathrm{sin}\:{q}\:=\:\mathrm{1}\:\mathrm{then}\:{x}^{\mathrm{2}} +\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\mathrm{sin}\:{q}\:=?\: \\ $$ Commented by benjo_mathlover last updated on 10/Jan/21 $$\:{x}\:=\:\frac{\mathrm{cos}\:^{\mathrm{2}} \frac{{q}}{\mathrm{2}}+\mathrm{sin}\:^{\mathrm{2}} \frac{{q}}{\mathrm{2}}+\mathrm{2sin}\:\frac{{q}}{\mathrm{2}}\mathrm{cos}\:\frac{{q}}{\mathrm{2}}}{\mathrm{cos}\:^{\mathrm{2}} \frac{{q}}{\mathrm{2}}−\mathrm{sin}\:^{\mathrm{2}}…
Question Number 63273 by mathmax by abdo last updated on 01/Jul/19 $${let}\:{F}\left({x}\right)\:=\int_{{x}^{\mathrm{2}} } ^{{x}^{\mathrm{3}} } \:\:\:\:\:\frac{{sin}\left({t}\right)}{{t}+{x}}\:{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:{F}\left({x}\right)\:{and}\:{lim}_{{x}\rightarrow+\infty} {F}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculste}\:{lim}_{{x}\rightarrow\mathrm{0}} \:{F}^{'} \left({x}\right)\:{and}\:{lim}_{{x}\rightarrow+\infty} \:{F}^{'}…
Question Number 128806 by LUFFY last updated on 10/Jan/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\left({n}^{\mathrm{2}} +{k}^{\mathrm{2}} \right)}\:=\:?????? \\ $$ Answered by Dwaipayan Shikari last updated on 10/Jan/21 $$\underset{{n}=\mathrm{1}}…
Question Number 128805 by bramlexs22 last updated on 10/Jan/21 $$\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{e}^{\mathrm{i}\theta} +\mathrm{1}\:=\:\mathrm{e}^{−\frac{\mathrm{i}\theta}{\mathrm{2}}} \:+\:\mathrm{e}^{\frac{\mathrm{i}\theta}{\mathrm{2}}} \:? \\ $$ Commented by mr W last updated on 10/Jan/21 $${LHS}=\left(\mathrm{1}+\mathrm{cos}\:\theta\right)+{i}\:\mathrm{sin}\:\theta \\…
Question Number 63268 by aliesam last updated on 01/Jul/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 63267 by Tawa1 last updated on 01/Jul/19 $$\:\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\:\left(\frac{\mathrm{n}^{\mathrm{3}} \:+\:\mathrm{1}}{\mathrm{n}^{\mathrm{3}} \:−\:\mathrm{1}}\right)^{\mathrm{2n}\:−\:\mathrm{n}^{\mathrm{3}} } \\ $$ Commented by Tawa1 last updated on 01/Jul/19 $$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\…
Question Number 63261 by aliesam last updated on 01/Jul/19 $$\int{x}\:{tan}\left({x}\right)\:{dx} \\ $$ Commented by kaivan.ahmadi last updated on 01/Jul/19 $${u}={tanx}\Rightarrow{du}=\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$$${dv}={xdx}\Rightarrow{v}=\frac{{x}^{\mathrm{2}} }{\mathrm{2}} \\…
Question Number 128797 by mnjuly1970 last updated on 10/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\phi\:\overset{???} {=}\int_{\mathrm{0}} ^{\:\infty} \left(\frac{{tanh}\left({x}\right)}{{e}^{{x}} }\right)\:{dx} \\ $$$$ \\ $$ Answered by Dwaipayan Shikari last…
Question Number 63256 by ajfour last updated on 01/Jul/19 Commented by ajfour last updated on 01/Jul/19 $${Find}\:{r}={OB},\:{such}\:{that}\:\bigtriangleup{ABC} \\ $$$${has}\:{maximum}\:{area}. \\ $$ Commented by ajfour last…
Question Number 128788 by bramlexs22 last updated on 10/Jan/21 $$\:\mathrm{Prove}\:\mathrm{that}\:\left(\mathrm{1}+\mathrm{tan}\:\mathrm{x}\right)\left(\mathrm{1}+\mathrm{tan}\:\mathrm{4x}\right)\:=\mathrm{2}? \\ $$ Commented by bramlexs22 last updated on 10/Jan/21 $$\mathrm{i}\:\mathrm{think}\:\mathrm{its}\:\mathrm{not}\:\mathrm{true}\:! \\ $$ Commented by mr…