Question Number 65092 by mathmax by abdo last updated on 25/Jul/19 $${calculate}\:\:\int\:\:\frac{\mathrm{1}}{{x}\:{cosx}}\prod_{{i}=\mathrm{1}} ^{{n}} \left(\mathrm{1}−{tan}^{\mathrm{2}} \left(\frac{{x}}{\mathrm{2}^{{i}} }\right)\right){dx} \\ $$ Commented by ~ À ® @ 237…
Question Number 130626 by Lordose last updated on 27/Jan/21 $$\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{x}^{\mathrm{4}} \mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{6}} }\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 65087 by Tawa1 last updated on 25/Jul/19 Answered by MJS last updated on 25/Jul/19 $$\mathrm{easier}\:\mathrm{than}\:\mathrm{it}\:\mathrm{seems} \\ $$$$\left(\mathrm{1}\right)\:\:{x}+{y}+{z}=\mathrm{0}\:\Rightarrow\:{z}=−{x}−{y} \\ $$$$\mathrm{insert}\:\mathrm{this}\:\mathrm{in}\:\left(\mathrm{2}\right)\:\mathrm{and}\:\left(\mathrm{3}\right) \\ $$$$\left(\mathrm{2}\right)\:−\mathrm{3}{xy}\left({x}+{y}\right)=\mathrm{18} \\ $$$$\left(\mathrm{3}\right)\:\:−\mathrm{7}{xy}\left({x}+{y}\right)\left({x}^{\mathrm{2}}…
Question Number 130619 by mohammad17 last updated on 27/Jan/21 $${solve}\:{the}\:{equation}\:{sinz}={i}\:? \\ $$ Answered by Dwaipayan Shikari last updated on 27/Jan/21 $$\frac{{e}^{{iz}} −{e}^{−{iz}} }{\mathrm{2}{i}}={i}\Rightarrow{e}^{\mathrm{2}{iz}} +\mathrm{2}{e}^{{iz}} −\mathrm{1}=\mathrm{0}\Rightarrow{e}^{{iz}}…
Question Number 130616 by bramlexs22 last updated on 27/Jan/21 $$\:\int\:\frac{\mathrm{dx}}{\mathrm{1}−\mathrm{k}.\mathrm{sin}\:\mathrm{x}}\:?\:\mathrm{where}\:\mid\mathrm{k}\mid<\mathrm{1} \\ $$ Answered by EDWIN88 last updated on 27/Jan/21 $$\:\mathrm{let}\:\mathrm{tan}\:\left(\frac{{x}}{\mathrm{2}}\right)=\:{s}\:\Rightarrow{x}\:=\mathrm{2arctan}\:{s} \\ $$$$\:{dx}\:=\:\frac{\mathrm{2}{ds}}{{s}^{\mathrm{2}} +\mathrm{1}}\:;\:\mathrm{sin}\:{x}\:=\:\mathrm{2tan}\:\left(\frac{{x}}{\mathrm{2}}\right)\mathrm{cos}\:^{\mathrm{2}} \left(\frac{{x}}{\mathrm{2}}\right) \\…
Question Number 65077 by naka3546 last updated on 24/Jul/19 Answered by MJS last updated on 25/Jul/19 $$\left(\mathrm{1}\right) \\ $$$${a}+{b}+\left({c}^{\mathrm{2}} −\mathrm{8}{c}+\mathrm{14}\right)\sqrt{{a}+{b}−\mathrm{2}}=\mathrm{1} \\ $$$$\sqrt{{a}+{b}−\mathrm{2}}={t}\Rightarrow{t}\geqslant\mathrm{0} \\ $$$$\Rightarrow\:{a}+{b}={t}^{\mathrm{2}} +\mathrm{2}…
Question Number 130607 by Study last updated on 27/Jan/21 $$\infty^{\infty} =? \\ $$ Commented by MJS_new last updated on 27/Jan/21 $$\infty^{\infty} =?\:\left(\mathrm{1}\:\mathrm{question}\:\mathrm{mark}!\:\Rightarrow\:\mathrm{easy}!!\right) \\ $$$$\mathrm{0}^{\mathrm{0}} =??\:\left(\mathrm{2}\:\mathrm{question}\:\mathrm{marks}!!!\:\Rightarrow\:\mathrm{medium}!!!!\right)…
Question Number 130604 by Study last updated on 27/Jan/21 $$\frac{{d}}{{dx}}\left({x}!\right)=??? \\ $$ Answered by Dwaipayan Shikari last updated on 27/Jan/21 $$\frac{{d}}{{dx}}\left({x}!\right)=\Gamma\left({x}+\mathrm{1}\right)\psi\left({x}+\mathrm{1}\right) \\ $$ Answered by…
Question Number 130605 by Study last updated on 27/Jan/21 $$\mathrm{0}^{\mathrm{0}} =?? \\ $$ Answered by mathmax by abdo last updated on 27/Jan/21 $$\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}^{+} } \:\mathrm{x}^{\mathrm{x}}…
Question Number 130602 by EDWIN88 last updated on 27/Jan/21 Answered by mr W last updated on 27/Jan/21 $$={number}\:{of}\:\mathrm{4}\:{digit}\:{numbers}\:{which} \\ $$$${are}\:{divisible}\:{by}\:\mathrm{3}: \\ $$$$\mathrm{1002},\:\mathrm{1005},\:…,\:\mathrm{9999} \\ $$$$\Rightarrow\frac{\mathrm{9999}−\mathrm{1002}}{\mathrm{3}}+\mathrm{1}=\mathrm{3000} \\…