Question Number 132741 by mnjuly1970 last updated on 16/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:\:\:{calculus}… \\ $$$$\:\:\int_{\mathrm{0}^{\:\:\:\:} \:\:} ^{\:\mathrm{1}} \frac{{dx}}{\left({x}−\mathrm{2}\right)\left({x}^{\mathrm{2}} \left(\mathrm{1}−{x}\right)^{\mathrm{3}} \right)^{\frac{\mathrm{1}}{\mathrm{5}}} }\:=? \\ $$ Commented by MJS_new last updated…
Question Number 1624 by 112358 last updated on 27/Aug/15 $${Find}\:{the}\:{first}\:{derivative}\:{of} \\ $$$${y}\left({x}\right)=\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+…}}}}} \\ $$$${from}\:{first}\:{principles}.\: \\ $$$$ \\ $$ Commented by Rasheed Soomro last updated on…
Question Number 1571 by 112358 last updated on 20/Aug/15 $$\int_{\mathrm{0}} ^{\:\infty} \frac{{e}^{−\mathrm{3}{x}^{\mathrm{2}} } }{{x}^{\mathrm{1}/\mathrm{5}} }{dx}=? \\ $$ Answered by prakash jain last updated on 20/Aug/15…
Question Number 132477 by KZ last updated on 14/Feb/21 $${define} \\ $$$${f}\left({x}.{y}\right)= \\ $$$$\left.\left\{\frac{\mathrm{xy}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \right)\:}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:{if}\:\left({x}.{y}\right)\neq\right)\mathrm{0}.\mathrm{0}\right) \\ $$$$\:\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{if}\:\left({x}.{y}\right)=\left(\mathrm{0}.\mathrm{0}\right) \\ $$$$ \\ $$$${show}\:{that}\:{f},\frac{\partial{f}}{\partial{x}}\:{and}\:\frac{\partial{f}}{\partial{y}\:\:}\:{are}\: \\…
Question Number 66922 by paro123 last updated on 20/Aug/19 Commented by paro123 last updated on 20/Aug/19 $$\mathrm{No}.\mathrm{8} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 132459 by mnjuly1970 last updated on 14/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….\:{nice}\:\:\:{calculus}\:…. \\ $$$$\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({x}^{\mathrm{2}} \right){ln}\left({x}\right)}{{x}^{\frac{\mathrm{3}}{\mathrm{2}}} }{dx}= \\ $$$$\:\:{solution}: \\ $$$$\boldsymbol{\phi}\overset{{x}^{\mathrm{2}} ={t}} {=}\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({t}\right){ln}\left(\sqrt{{t}}\:\right)}{{t}^{\frac{\mathrm{3}}{\mathrm{4}}} }\:\frac{{dt}}{{t}^{\frac{\mathrm{1}}{\mathrm{2}}}…
Question Number 132444 by liberty last updated on 14/Feb/21 Answered by bemath last updated on 14/Feb/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 132440 by liberty last updated on 14/Feb/21 $$\mathrm{A}\:\mathrm{vessel}\:\mathrm{containing}\:\mathrm{water}\:\mathrm{has}\:\mathrm{the}\: \\ $$$$\mathrm{shape}\:\mathrm{of}\:\mathrm{and}\:\mathrm{inverted}\:\mathrm{right}\:\mathrm{circular} \\ $$$$\mathrm{cone}\:\mathrm{with}\:\mathrm{base}\:\mathrm{radius}\:\mathrm{2m}\:\mathrm{and}\:\mathrm{height}\:\mathrm{5m} \\ $$$$\mathrm{The}\:\mathrm{water}\:\mathrm{flows}\:\mathrm{from}\:\mathrm{the}\:\mathrm{apex} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{cone}\:\mathrm{at}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{rate}\: \\ $$$$\mathrm{of}\:\mathrm{0}.\mathrm{2}\:\mathrm{m}^{\mathrm{3}} /\mathrm{min}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{at} \\ $$$$\mathrm{which}\:\mathrm{the}\:\mathrm{water}\:\mathrm{level}\:\mathrm{is}\:\mathrm{dropping} \\ $$$$\mathrm{when}\:\mathrm{the}\:\mathrm{depth}\:\mathrm{of}\:\mathrm{the}\:\mathrm{water}\:\mathrm{is}…
Question Number 132407 by bramlexs22 last updated on 14/Feb/21 $$\mathrm{on}\:\mathrm{circle}\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{25}\:,\:\mathrm{find}\:\mathrm{the}\:\mathrm{point} \\ $$$$\mathrm{closest}\:\mathrm{to}\:\left(\mathrm{1},\mathrm{1}\right). \\ $$ Answered by EDWIN88 last updated on 14/Feb/21 $$\mathrm{let}\:\mathrm{P}\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{be}\:\mathrm{a}\:\mathrm{point}\:\mathrm{on}\:\mathrm{a}\:\mathrm{circle}\: \\…
Question Number 66866 by rajesh4661kumar@gmail.com last updated on 20/Aug/19 Commented by mathmax by abdo last updated on 20/Aug/19 $${first}\:\:{x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }>\mathrm{0}\:\:{for}\:{all}\:{x}\:{so}\:{y}={ln}\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)={argsh}\left({x}\right)\:\Rightarrow \\ $$$${y}^{'} \left({x}\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:=\left(\mathrm{1}+{x}^{\mathrm{2}}…