Question Number 149339 by mnjuly1970 last updated on 04/Aug/21 $$\:\:\:\:\:\:\:\:\:\:…{nice}……{mathematics}… \\ $$$$\:\:\:\:\:\:{ln}\left(\:\mathrm{2}\right)\:−\underset{{n}=\mathrm{1}\:} {\overset{\infty} {\sum}}\frac{\zeta\:\left(\:\mathrm{2}{n}+\mathrm{1}\:\right)−\mathrm{1}}{{n}\:+\:\mathrm{1}}\:=\:? \\ $$$$\:\:\:\:….{m}.{n}…. \\ $$ Answered by Kamel last updated on 04/Aug/21…
Question Number 83782 by jagoll last updated on 06/Mar/20 $$\mathrm{f}^{\left(\mathrm{5}\right)} \:\left(\mathrm{x}\right)\:=\:\mathrm{4}^{−\mathrm{sin}\:\mathrm{x}} \\ $$$$\mathrm{f}^{\left(\mathrm{7}\right)} \left(\mathrm{x}\right)\:=?\: \\ $$ Commented by john santu last updated on 06/Mar/20 $$\mathrm{f}^{\left(\mathrm{n}\right)}…
Question Number 149252 by holomata last updated on 04/Aug/21 $$ \\ $$$${e}^{{y}} =\left(\mathrm{sin}\:{x}\right)\left(\mathrm{cos}\:{x}\right) \\ $$$${find}\:\frac{{dy}}{{dx}} \\ $$ Answered by Mokmokhi last updated on 04/Aug/21 $$\frac{{dy}}{{dx}}=\mathrm{2cot}\:\mathrm{2}{x}…
Question Number 149191 by mnjuly1970 last updated on 03/Aug/21 $$\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:……{calculus}….. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{{sech}\left(\pi{x}\right)}{\mathrm{1}+\mathrm{4}{x}^{\:\mathrm{2}} }\:{dx}=? \\ $$$$\:………{m}.{n}… \\ $$ Answered by mindispower last…
Question Number 83653 by jagoll last updated on 05/Mar/20 $$\mathrm{find}\:\mathrm{range}\:\mathrm{of}\:\mathrm{function}\: \\ $$$$\mathrm{y}=\:\frac{\mathrm{4}}{\left({x}^{\mathrm{2}} −\mathrm{4}\right)} \\ $$ Answered by MJS last updated on 05/Mar/20 $${x}=\pm\mathrm{2}\sqrt{\frac{{y}+\mathrm{1}}{{y}}} \\ $$$$\Rightarrow\:{y}\leqslant−\mathrm{1}\vee{y}>\mathrm{0}…
Question Number 83649 by 698148290 last updated on 04/Mar/20 Answered by MJS last updated on 05/Mar/20 $$=\int\frac{\sqrt{\mathrm{1}−{x}}}{{x}}{dx}+\int\frac{\sqrt{\mathrm{2}−{x}^{\mathrm{2}} }}{{x}}{dx}+\int\frac{\sqrt{\mathrm{4}−{x}^{\mathrm{4}} }}{{x}}{dx} \\ $$$$\mathrm{substitute} \\ $$$${u}=\sqrt{\mathrm{1}−{x}}\:\rightarrow\:{dx}=−\mathrm{2}\sqrt{\mathrm{1}−{x}}{du} \\ $$$${v}=\sqrt{\mathrm{2}−{x}^{\mathrm{2}}…
Question Number 83639 by niroj last updated on 04/Mar/20 $$ \\ $$$$\: \\ $$$$\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equations}}: \\ $$$$\:\:\:\left(\mathrm{i}\right)\:\mathrm{log}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)=\mathrm{ax}+\mathrm{by} \\ $$$$\:\:\:\left(\mathrm{ii}\right)\:\mathrm{x}\:\mathrm{cos}\:\mathrm{y}\:\mathrm{dy}=\left(\mathrm{x}\:\mathrm{e}^{\mathrm{x}} \mathrm{log}\:\mathrm{x}\:+\mathrm{e}^{\mathrm{x}} \right)\mathrm{dx} \\ $$$$ \\ $$ Answered…
Question Number 149077 by mnjuly1970 last updated on 02/Aug/21 $$ \\ $$$$\:\:\:\:\:\:\Omega\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{ln}\:\left(\:\mathrm{1}+\:\sqrt{{x}}\:\right)}{\mathrm{1}+{x}}\:{dx}\:=? \\ $$$$\:…..{m}.{n}….. \\ $$ Answered by mindispower last updated on 02/Aug/21…
Question Number 83520 by john santu last updated on 03/Mar/20 $$\mathrm{closest}\:\mathrm{distance}\:\mathrm{point}\:\left(\mathrm{6},\mathrm{9}\right)\: \\ $$$$\mathrm{to}\:\mathrm{curve}\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{2}} −\mathrm{12x}+\mathrm{32}\:. \\ $$$$\mathrm{mister}\:\mathrm{w}\:\mathrm{your}\:\mathrm{method}\:\mathrm{can}\:\mathrm{be}\: \\ $$$$\mathrm{applied}\:\mathrm{to}\:\mathrm{this}\:\mathrm{problem}? \\ $$ Answered by john santu last…
Question Number 83511 by jagoll last updated on 03/Mar/20 $$\mathrm{find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mid\mathrm{x}−\mathrm{y}\mid\:+\sqrt{\left(\mathrm{x}−\mathrm{3}\right)^{\mathrm{2}} +\left(\mathrm{y}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Answered by john santu last updated on 03/Mar/20 $$\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{we}\:\mathrm{get}\:\mathrm{when}\:…