Question Number 136070 by Dwaipayan Shikari last updated on 18/Mar/21 $$\frac{{sin}\left(\sqrt{\mathrm{2}}\right)}{\mathrm{1}^{\mathrm{3}} }+\frac{{sin}\left(\mathrm{2}\sqrt{\mathrm{2}}\right)}{\mathrm{2}^{\mathrm{3}} }+\frac{{sin}\left(\mathrm{3}\sqrt{\mathrm{2}}\right)}{\mathrm{3}^{\mathrm{3}} }+…=\frac{\pi^{{b}} +\mathrm{1}}{\:{a}\sqrt{{b}}}−\frac{\pi}{{b}} \\ $$$${Find}\:{a}−{b} \\ $$ Answered by mnjuly1970 last updated on…
Question Number 136064 by bramlexs22 last updated on 18/Mar/21 $$\:\:\:\:\:\mathrm{3}^{\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{3}^{{x}} −\mathrm{1}\right)} \:=\:\mathrm{2}^{\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{2}^{{x}} +\mathrm{1}\right)} +\:\mathrm{1} \\ $$ Answered by Kintinu last updated on 18/Mar/21…
Question Number 136067 by bramlexs22 last updated on 18/Mar/21 $$\Lambda\:=\:\int\:{x}^{\mathrm{3}} \:\left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{10}} \:{dx}\: \\ $$ Answered by Olaf last updated on 18/Mar/21 $$\Lambda\:=\:\int{x}^{\mathrm{3}} \left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{10}}…
Question Number 4993 by love math last updated on 29/Mar/16 $${f}\left({x}\right)=\frac{{x}\:{ln}\:{x}}{\mathrm{1}+\:{e}^{{x}} } \\ $$$$ \\ $$$${f}\:'\left({x}\right)\:−\:? \\ $$ Answered by FilupSmith last updated on 30/Mar/16…
Question Number 4992 by love math last updated on 29/Mar/16 $${f}\left({x}\right)=\mathrm{2}{x}\:{e}^{{x}} \\ $$$${f}\:'\left({x}\right)\:−? \\ $$ Answered by FilupSmith last updated on 29/Mar/16 $${f}\left({x}\right)={uv} \\ $$$${f}\left({x}\right)={uv}'+{u}'{v}…
Question Number 136060 by mnjuly1970 last updated on 18/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…{advanced}\:\:\:{calculus}…. \\ $$$$\:\:\:\:{evaluate}:: \\ $$$$\:\:\:\:\boldsymbol{\phi}=\mathrm{Im}\left(\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {li}_{\mathrm{2}} \left({sin}\left({x}\right)\right)+{li}_{\mathrm{2}} \left({csc}\left({x}\right)\right){dx}\right) \\ $$$$ \\ $$ Answered by mindispower…
Question Number 136063 by liberty last updated on 18/Mar/21 $$ \\ $$A and B can do a job in 10 days and 5 days, respectively.…
Question Number 70525 by Rasheed.Sindhi last updated on 05/Oct/19 $${If}\:{x},{y},{z}\:{is}\:{a}\:{primitive}\:{Pythagorean} \\ $$$${triple},{prove}\:{that}\:{x}+{y}\:{and}\:{x}−{y}\:{are} \\ $$$${congruent}\:{modulo}\:\mathrm{8}\:{to}\:{either}\:\mathrm{1}\:{or}\:\mathrm{7}. \\ $$ Answered by mind is power last updated on 07/Oct/19…
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Question Number 70518 by Shamim last updated on 05/Oct/19 $$\mathrm{If}\:\mathrm{a}^{\mathrm{3}} −\mathrm{b}^{\mathrm{3}} =\:\mathrm{513}\:\mathrm{and}\:\mathrm{ab}=\:\mathrm{54}\:\mathrm{then}\:\mathrm{find}\: \\ $$$$\mathrm{a}−\mathrm{b}=\:? \\ $$ Commented by Prithwish sen last updated on 05/Oct/19 $$\boldsymbol{\mathrm{use}}\:\:\:\left(\boldsymbol{\mathrm{a}}−\boldsymbol{\mathrm{b}}\right)^{\mathrm{3}}…