Question Number 26073 by gopikrishnan005@gmail.com last updated on 19/Dec/17 $$ \\ $$$${solve}\:{the}\:{differential}\:{equation}\left({D}^{\mathrm{2}} +\mathrm{2}{D}+\mathrm{1}\right){y}={x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1} \\ $$ Commented by gopikrishnan005@gmail.com last updated on 20/Dec/17 $${pls}\:{explain} \\…
Question Number 157116 by cortano last updated on 20/Oct/21 $$\:{max}\:\wedge\:{min}\:{of}\:{f}\left({x}\right)\:=\sqrt{{x}}\:+\mathrm{4}\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{2}}} \\ $$ Commented by cortano last updated on 20/Oct/21 $${without}\:{derivative} \\ $$ Commented by mr…
Question Number 91460 by M±th+et+s last updated on 30/Apr/20 $${one}\:{of}\:{the}\:{conditions}\:{of}\:{the}\:{inflection} \\ $$$${point}\:{is}\:{inflection}\:{tangent}. \\ $$$${what}\:{is}\:{inflection}\:{tangent}? \\ $$ Answered by MJS last updated on 01/May/20 $$\mathrm{it}'\mathrm{s}\:\mathrm{the}\:\mathrm{tangent}\:\mathrm{in}\:\mathrm{the}\:\mathrm{inflection}\:\mathrm{point}\:\mathrm{which} \\…
Question Number 25845 by NECx last updated on 15/Dec/17 $${using}\:{the}\:\mathrm{1}{st}\:{principle}\:{find}\:{the} \\ $$$${derivative}\:{of}\: \\ $$$$\:\:\:\:\:{y}=\left({ax}+{b}\right)^{{n}} \\ $$ Answered by ajfour last updated on 15/Dec/17 $$\frac{{dy}}{{dx}}=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left({ax}+{ah}+{b}\right)^{{n}}…
Question Number 156864 by mnjuly1970 last updated on 16/Oct/21 $$ \\ $$$$\:\:\:\:\phi\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{ln}\:\left(\mathrm{1}−{x}^{\:\mathrm{2}} \right)}{\mathrm{1}+\:{x}^{\:\mathrm{2}} }\:{dx}\:= \\ $$$$\:\:{proof}\:: \\ $$$$\:\:\:\:\phi\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{ln}\left(\mathrm{1}−{x}\:\right)}{\mathrm{1}+{x}^{\:\mathrm{2}} }{dx}\:+\:\frac{\pi}{\mathrm{8}}{ln}\left(\mathrm{2}\right) \\ $$$$\:\:\:\:….\:\mathrm{I}=\:\int_{\mathrm{0}}…
Question Number 91329 by niroj last updated on 29/Apr/20 $$\:\mathrm{S}\boldsymbol{\mathrm{olve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\:\:\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }\:−\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}+\boldsymbol{\mathrm{xy}}\:=\:\boldsymbol{\mathrm{x}} \\ $$ Commented by MWSuSon last updated on 30/Apr/20 $${do}\:{you}\:{need}\:{a}\:{specific}\:{method}?…
Question Number 156824 by Tawa11 last updated on 15/Oct/21 $$\mathrm{If}\:\:\:\:\:\:\mathrm{x}\:\:\:−\:\:\:\mathrm{z}\:\:\:\:=\:\:\:\:\mathrm{tan}^{−\:\mathrm{1}} \left(\mathrm{yz}\right)\:\:\:\:\:\mathrm{and}\:\:\:\:\:\:\mathrm{z}\:\:\:=\:\:\:\mathrm{z}\left(\mathrm{x},\:\:\mathrm{y}\right),\:\:\:\:\:\:\mathrm{find}\:\:\:\:\frac{\delta\mathrm{z}}{\delta\mathrm{x}}\:,\:\:\:\frac{\delta\mathrm{z}}{\delta\mathrm{y}} \\ $$ Answered by mr W last updated on 16/Oct/21 $$\mathrm{1}−\frac{\partial{z}}{\partial{x}}=\frac{{y}}{\mathrm{1}+{y}^{\mathrm{2}} {z}^{\mathrm{2}} }×\frac{\partial{z}}{\partial{x}} \\…
Question Number 156776 by mnjuly1970 last updated on 15/Oct/21 $$ \\ $$$$\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left({n}\:{ln}\left(\frac{\mathrm{2}{n}+\mathrm{1}}{\mathrm{2}{n}−\mathrm{1}}\right)\:−\mathrm{1}\right)=? \\ $$$$ \\ $$ Commented by CAIMAN last updated on 15/Oct/21…
Question Number 91185 by Tony Lin last updated on 28/Apr/20 $${f}\left({x}\right)=\left({x}−\mathrm{3}\right)^{\mathrm{5}} {ln}\left(\mathrm{1}+{x}\right) \\ $$$${f}^{\left(\mathrm{2020}\right)} \left(\mathrm{3}\right)=? \\ $$ Commented by Tony Lin last updated on 28/Apr/20…
Question Number 25572 by hoangnampham13 last updated on 11/Dec/17 $${Solve}\:{the}\:{differential}\:{equation}: \\ $$$${y}'\:=\:{cosh}\left({x}+{y}\right) \\ $$ Answered by prakash jain last updated on 11/Dec/17 $${y}'\:=\:{cosh}\left({x}+{y}\right)\:\:\:\left({A}\right) \\ $$$${u}\left({x}\right)={y}\left({x}\right)+{x}…