Question Number 136682 by snipers237 last updated on 24/Mar/21 $$\:{Im}\left(\int_{{C}^{+} \left(\mathrm{0},\frac{\mathrm{1}}{\mathrm{2}}\right)} \overset{−} {{z}dz}\:\right)=\:\frac{\pi}{\mathrm{2}}\:\: \\ $$ Answered by Olaf last updated on 24/Mar/21 $$\Omega\:=\:\mathrm{Im}\int_{\mathrm{C}^{+} \left(\mathrm{0},\frac{\mathrm{1}}{\mathrm{2}}\right)} \overset{−}…
Question Number 5513 by 314159 last updated on 17/May/16 $${If}\:{n}>\mathrm{1},\:{prove}\:{by}\:{mathematical}\:{induction}\:{that} \\ $$$${n}\left(\left({n}+\mathrm{1}\right)^{\frac{\mathrm{1}}{{n}}} −\mathrm{1}\right)\:<\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+…\frac{\mathrm{1}}{{n}}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 136581 by mnjuly1970 last updated on 23/Mar/21 $$\:\:\:\:\:\:\:\:…….{advanced}\:\:\:{calculus}…. \\ $$$$\:\:\:{pove}\:{that}:: \\ $$$$:::\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left\{\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{2}^{\mathrm{2}{n}} }\begin{pmatrix}{\:\mathrm{2}{n}}\\{\:\:{n}}\end{pmatrix}\:{cos}\left({nx}\right)\right\}=\frac{{cos}\left(\frac{{x}}{\mathrm{4}}\right)}{\:\sqrt{\mathrm{2}{cos}\left(\frac{{x}}{\mathrm{2}}\right)}} \\ $$ Answered by Dwaipayan Shikari last…
Question Number 136570 by mnjuly1970 last updated on 23/Mar/21 $$\:\:\:\:\:\:\:\:\:…….{nice}\:\:…..\:\:\:{calculus}….. \\ $$$$\:\:\:\:\Omega=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}{cos}^{{n}} \left({x}\right).{cos}\left({nx}\right)=? \\ $$$$\:\:\:{solution}:::: \\ $$$$\:\:\:\:\Omega=\frac{\mathrm{1}}{\mathrm{2}}\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}{cos}^{{n}−\mathrm{1}} \left({x}\right)\left\{{cos}\left({x}−{nx}\right)+{cos}\left({x}+{nx}\right)\right. \\ $$$$\:\:\therefore\:\mathrm{2}\Omega=\underset{{n}=\mathrm{0}} {\overset{\infty}…
Question Number 136555 by mnjuly1970 last updated on 23/Mar/21 $$\:\:\:\:\:\:\:\:\:….{nice}\:\:\:\:……\:\:\:{calculus}…. \\ $$$$\:\:\:{prove}\:{that} \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}=\frac{\pi}{\mathrm{2}}{ln}\left(\mathrm{2}\right)−\frac{\pi}{\mathrm{4}} \\ $$$$\:\:\:\:\::::::::: \\ $$ Answered by…
Question Number 5456 by 3 last updated on 15/May/16 $$\precnapprox \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 5365 by sanusihammed last updated on 11/May/16 $${If}\:\:{y}\:=\:{x}^{{x}^{{x}^{{x}} } } \:\:\:.\:\:{Find}\:{dy}/{dx} \\ $$ Answered by Yozzii last updated on 11/May/16 $${lny}={x}^{{x}^{{x}} } {lnx}\:\:\:\left({x}>\mathrm{0}\right)…
Question Number 136295 by mnjuly1970 last updated on 20/Mar/21 $$\:\:\:\:\:\:….{nice}\:\:{calculus}… \\ $$$${prove}\::: \\ $$$$\mathrm{1}\:::\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{tan}^{−\mathrm{1}} \left(\sqrt{{tan}\left({x}\right)}\:\right)}{{tan}\left({x}\right)}{dx}=\frac{\pi}{\mathrm{2}}{log}\left(\mathrm{2}+\sqrt{\mathrm{2}}\:\right) \\ $$$$\mathrm{2}::\Omega=\int_{−\pi} ^{\:\pi} \frac{{e}^{\left({sin}\left({x}\right)+{cos}\left({x}\right)\right)} {cos}\left({sin}\left({x}\right)\right)}{{e}^{{x}} +{e}^{{sin}\left({x}\right)} }{dx}=\pi \\…
Question Number 136284 by liberty last updated on 20/Mar/21 $${What}\:{is}\:{shortest}\:{distance}\: \\ $$$${from}\:{A}\left(\mathrm{3},\mathrm{8}\right)\:{to}\:{the}\:{circle}\: \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{4}{x}−\mathrm{6}{y}\:=\:\mathrm{12}\: \\ $$ Answered by EDWIN88 last updated on 20/Mar/21…
Question Number 70741 by aliesam last updated on 07/Oct/19 $${f}\left({x}\right)=\begin{cases}{{x}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}\leqslant\mathrm{1}}\\{}\\{\mid{x}−\mathrm{2}\mid\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}>\mathrm{1}}\end{cases} \\ $$$$ \\ $$$${find}\:{the}\:{critical}\:{points} \\ $$ Commented by kaivan.ahmadi last updated on 07/Oct/19 $${f}\left({x}\right)=\begin{cases}{{x}^{\mathrm{2}}…