Question Number 126478 by BHOOPENDRA last updated on 20/Dec/20 $${find}\:\frac{\partial{w}}{\partial\theta}\:{and}\:\frac{\partial{w}}{\partial\phi}\:{given}\:{that}\: \\ $$$${w}\left({x},{y},{z}\right)={f}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)\:{where}\:{x}={rcos}\theta{cos}\phi \\ $$$${y}={rcos}\theta{sin}\phi,{z}={rsin}\theta. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 126476 by mnjuly1970 last updated on 20/Dec/20 $$\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:{calculate}\::: \\ $$$$\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \:\frac{{tanh}\left(\pi{x}\right)}{{x}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}\:{dx}=? \\ $$ Answered by mathmax by abdo last…
Question Number 126440 by mnjuly1970 last updated on 20/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:{calculus}… \\ $$$$\:\:\:\:{prove}\:\:{that}\:::: \\ $$$$\:\:\:\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\prod}}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}^{\mathrm{4}} }\:\right)=\frac{{cosh}\left(\sqrt{\mathrm{2}}\:\pi\right)−{cos}\left(\sqrt{\mathrm{2}}\:\pi\right)}{\mathrm{4}\pi^{\mathrm{2}} } \\ $$$$ \\ $$ Answered by Dwaipayan…
Question Number 191859 by mathlove last updated on 02/May/23 Commented by mr W last updated on 03/May/23 $${all}\:{are}\:{of}\:{type}\:{y}'+{P}\left({x}\right){y}={Q}\left({x}\right). \\ $$ Answered by qaz last updated…
Question Number 191796 by mathlove last updated on 30/Apr/23 Commented by mathlove last updated on 01/May/23 $${pleas}\:{solve}\:{this} \\ $$ Answered by AST last updated on…
Question Number 60695 by maxmathsup by imad last updated on 24/May/19 $${solve}\:\sqrt{\mathrm{3}+{x}^{\mathrm{2}} }{y}^{''} \:\:\:\:−\left(\mathrm{2}{x}+\mathrm{1}\right){y}^{'} \:={x}^{\mathrm{2}} \:{e}^{−{x}^{\mathrm{2}} \:\:\:} \\ $$ Commented by maxmathsup by imad last…
Question Number 126070 by benjo_mathlover last updated on 17/Dec/20 Commented by liberty last updated on 17/Dec/20 $${h}\left({x}\right)=\int_{\mathrm{1}} ^{\:{x}} {f}\left({t}\right)\:{dt}\:\Leftrightarrow\:{h}'\left({x}\right)=\:{f}\left({x}\right) \\ $$$${h}'\left(\mathrm{4}\right)={f}\left(\mathrm{4}\right)=\:\mathrm{2} \\ $$$$ \\ $$…
Question Number 126039 by snipers237 last updated on 16/Dec/20 $${Let}\:{A}=\left[\mathrm{2};\infty\left[^{\mathrm{2}} \:\:{and}\:{f}\:\in\left(\mathbb{R}×\mathbb{R}\right)^{\mathbb{R}} \:{such}\:{as}\:\right.\right. \\ $$$${f}\left({x},{y}\right)=\frac{\chi_{{A}} \left({x},{y}\right)}{{E}\left({x}\right)^{{E}\left({y}\right)} }\:\:{where}\:\chi_{{A}} \:{is}\:{the}\:{caracteristic}\:{function}\:{of}\:{A} \\ $$$$\:{Prove}\:{that}\:{f}\:{is}\:{a}\:{density}\:{of}\:{a}\:{probability}\:{P} \\ $$ Answered by mindispower last…
Question Number 126010 by bramlexs22 last updated on 16/Dec/20 Answered by liberty last updated on 16/Dec/20 $${The}\:{area}\:{of}\:{a}\:{tringle}\:{is}\:{A}=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{8}\right)\left(\mathrm{6}\right)\mathrm{sin}\:\theta \\ $$$${A}\:=\:\mathrm{24}\:\mathrm{sin}\:\theta \\ $$$$\frac{{dA}}{{dt}}\:=\:\left(\mathrm{24}\:\mathrm{cos}\:\theta\right)\:\frac{{d}\theta}{{dt}}\:;\:{where}\:\frac{{d}\theta}{{dt}}\:=\:\mathrm{0}.\mathrm{12}\:{rad}/{sec} \\ $$$$\Leftrightarrow\:\frac{{dA}}{{dt}}\:=\:\mathrm{24}×\mathrm{0}.\mathrm{12}×\mathrm{cos}\:\frac{\pi}{\mathrm{6}}=\:\mathrm{2}.\mathrm{49}\:{m}^{\mathrm{2}} /{sec}\: \\…
Question Number 126008 by bramlexs22 last updated on 16/Dec/20 $$\:{Find}\:{all}\:{asymptotes}\:{of}\:{the}\: \\ $$$${function}\:{y}=\frac{{x}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}}\:. \\ $$ Answered by liberty last updated on 16/Dec/20 $${Horizontal}\:{asymptote}\::\:{y}\:=\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{x}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}}\:=\:\underset{{x}\rightarrow\infty}…