Question Number 141581 by qaz last updated on 20/May/21 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{n}} }{\mathrm{1}+{x}}{dx}=? \\ $$ Commented by Dwaipayan Shikari last updated on 20/May/21…
Question Number 141580 by learner001 last updated on 20/May/21 $${i}\:{am}\:{finding}\:{it}\:{difficult}\:{to}\:{form}\:{a}\:{pde} \\ $$$${from}\:{the}\:{function}\:{f}\left({x}+{y}+{z},\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 10510 by ajfour last updated on 15/Feb/17 Answered by mrW1 last updated on 15/Feb/17 $$\mathrm{2sin}\:{x}+\mathrm{3cos}\:{x} \\ $$$$=\sqrt{\mathrm{13}}×\left(\frac{\mathrm{2}}{\:\sqrt{\mathrm{13}}}\mathrm{sin}\:{x}+\frac{\mathrm{3}}{\:\sqrt{\mathrm{13}}}\mathrm{cos}\:{x}\right) \\ $$$$=\sqrt{\mathrm{13}}×\left(\mathrm{sin}\:{x}\mathrm{cos}\:{t}+\mathrm{cos}\:{x}\mathrm{sin}\:{t}\right) \\ $$$$=\sqrt{\mathrm{13}}×\mathrm{sin}\:\left({x}+{t}\right) \\ $$$${with}\:{t}=\mathrm{sin}^{−\mathrm{1}}…
Question Number 141577 by qaz last updated on 20/May/21 $$\left(\frac{\mathrm{1}}{\mathrm{1}\centerdot\mathrm{2}\centerdot\mathrm{3}}\right)^{\mathrm{2}} +\left(\frac{\mathrm{1}}{\mathrm{2}\centerdot\mathrm{3}\centerdot\mathrm{4}}\right)^{\mathrm{2}} +\left(\frac{\mathrm{1}}{\mathrm{3}\centerdot\mathrm{4}\centerdot\mathrm{5}}\right)^{\mathrm{2}} +…=\frac{\mathrm{1}}{\mathrm{16}}\left(\mathrm{4}\pi^{\mathrm{2}} −\mathrm{39}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 10507 by Saham last updated on 14/Feb/17 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 141578 by Khalmohmmad last updated on 20/May/21 $$\int\sqrt{\mathrm{1}+\frac{\mathrm{1}}{{x}}}{dx}=? \\ $$ Answered by bramlexs22 last updated on 20/May/21 $$\:\int\:\frac{\sqrt{\mathrm{1}+{x}}}{\:\sqrt{{x}}}\:{dx}\: \\ $$$$\:{let}\:\sqrt{\mathrm{1}+{x}}\:=\:{u}\:\Rightarrow{x}={u}^{\mathrm{2}} −\mathrm{1}\: \\ $$$${dx}\:=\:\mathrm{2}{u}\:{du}\:…
Question Number 76038 by Crabby89p13 last updated on 22/Dec/19 Answered by JDamian last updated on 22/Dec/19 $$−\frac{\mathrm{3}}{\mathrm{13}}\:\left({A}\right) \\ $$ Commented by Crabby89p13 last updated on…
Question Number 141574 by sarkor last updated on 20/May/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 76037 by Crabby89p13 last updated on 22/Dec/19 $${Prove}\:{That} \\ $$$$\mathrm{sin}\:\mathrm{3}°\mathrm{sin}\:\mathrm{39}°\mathrm{sin}\:\mathrm{75}°=\mathrm{sin}\:\mathrm{9}°\mathrm{sin}\:\mathrm{24}°\mathrm{sin}\:\mathrm{30}° \\ $$ Answered by MJS last updated on 23/Dec/19 $$\mathrm{sin}\:\mathrm{3}\:=\mathrm{sin}\:\left(\mathrm{75}−\mathrm{2}×\mathrm{36}\right)\:= \\ $$$$=\mathrm{2cos}^{\mathrm{2}} \:\mathrm{36}\:\mathrm{sin}\:\mathrm{75}\:−\mathrm{2sin}\:\mathrm{36}\:\mathrm{cos}\:\mathrm{36}\:\mathrm{cos}\:\mathrm{75}\:−\mathrm{sin}\:\mathrm{75}\:=…
Question Number 141569 by SOMEDAVONG last updated on 20/May/21 $$\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}}\left(\frac{\mathrm{110}^{\mathrm{2}} }{\left(\mathrm{11}−\mathrm{10}\right)\left(\mathrm{11}^{\mathrm{2}} −\mathrm{10}^{\mathrm{2}} \right)}\:+\:\frac{\mathrm{110}^{\mathrm{2}} }{\left(\mathrm{11}^{\mathrm{2}} −\mathrm{10}^{\mathrm{2}} \right)\left(\mathrm{11}^{\mathrm{3}} −\mathrm{10}^{\mathrm{3}} \right)}\:+\:….+\:\frac{\mathrm{110}^{\mathrm{2}} }{\left(\mathrm{11}^{\mathrm{n}} −\mathrm{10}^{\mathrm{n}} \right)\left(\mathrm{11}^{\mathrm{n}+\mathrm{1}} −\mathrm{10}^{\mathrm{n}+\mathrm{1}} \right)}\right) \\…