Question Number 130884 by LYKA last updated on 30/Jan/21 $${let}\:{f}\left({x}.{y}\right)=\left[{x}^{\mathrm{2}} +{xy},{x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right]\: \\ $$$$ \\ $$$${prove}\:{from}\:{defination}\:{of}\: \\ $$$${derivative}\:{that}\:: \\ $$$${Df}_{\left({x},{y}\right)} \left(\mathrm{1},\mathrm{2}\right)=\left[\mathrm{4}\boldsymbol{{x}}+\boldsymbol{{y}},−\mathrm{2}{x}+\mathrm{4}{y}\right] \\ $$$$ \\…
Question Number 65300 by rajesh4661kumar@gmail.com last updated on 28/Jul/19 Commented by kaivan.ahmadi last updated on 28/Jul/19 $${f}\left({x}+\Delta{x}\right)={f}\left({x}\right)+{f}'\left({x}\right).\Delta{x} \\ $$$${f}\left({x}\right)={logx}\Rightarrow{f}'\left({x}\right)=\frac{\mathrm{1}}{{xln}\mathrm{10}} \\ $$$$\left.{f}\left(\mathrm{10}.\mathrm{02}\right)\right)={f}\left(\mathrm{10}+\mathrm{0}.\mathrm{02}\right)={f}\left(\mathrm{10}\right)+{f}'\left(\mathrm{10}\right)×\mathrm{0}.\mathrm{02}= \\ $$$$\mathrm{2}.\mathrm{3026}+\frac{\mathrm{1}}{\mathrm{10}{ln}\mathrm{10}}×\mathrm{0}.\mathrm{02}=\mathrm{2}.\mathrm{3026}+\frac{\mathrm{2}}{\mathrm{1000}{ln}\mathrm{10}} \\ $$$$…
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Question Number 65270 by Waseem Ahmad bhat last updated on 27/Jul/19 $${d}/{dx}\:{x}−\mathrm{2} \\ $$ Answered by Tanmay chaudhury last updated on 27/Jul/19 $${y}={x}−\mathrm{2} \\ $$$${y}+\bigtriangleup{y}=\left({x}+\bigtriangleup{x}\right)−\mathrm{2}…
Question Number 130780 by LYKA last updated on 28/Jan/21 Commented by kaivan.ahmadi last updated on 29/Jan/21 $$\overset{\rightarrow} {{b}}=\left(\mathrm{2},−\mathrm{1},\mathrm{1}\right)\Rightarrow\mid\overset{\rightarrow} {{b}}\mid=\sqrt{\mathrm{6}}\Rightarrow\overset{\rightarrow} {{u}}=\frac{\overset{\rightarrow} {{b}}}{\mid\overset{\rightarrow} {{b}}\mid}=\left(\frac{\mathrm{2}}{\:\sqrt{\mathrm{6}}},\frac{−\mathrm{1}}{\:\sqrt{\mathrm{6}}},\frac{\mathrm{1}}{\:\sqrt{\mathrm{6}}}\right) \\ $$$$\bigtriangledown{f}=\left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{3}{yz},\mathrm{3}{y}^{\mathrm{2}}…
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Question Number 130692 by mnjuly1970 last updated on 28/Jan/21 $$\:….\:{ordinary}\:{differential}\:{equation}…. \\ $$$$\:{find}\:{the}\:{general}\:{solution}\::: \\ $$$$\:\:\:\:\:\:\frac{{dy}}{{dx}}={e}^{{y}} {cos}\left({x}\right)+{cot}\left({x}\right) \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 130582 by bramlexs22 last updated on 27/Jan/21 $$\mathrm{A}\:\mathrm{metal}\:\mathrm{rain}\:\mathrm{gutter}\:\mathrm{is}\:\mathrm{to}\:\mathrm{have}\:\mathrm{3}−\mathrm{inch}\:\mathrm{and} \\ $$$$\mathrm{a}\:\mathrm{3}−\mathrm{inch}\:\mathrm{bottom}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{making}\:\mathrm{an}\:\mathrm{equal} \\ $$$$\mathrm{angle}\:\theta\:\mathrm{with}\:\mathrm{the}\:\mathrm{bottom}.\:\mathrm{What}\:\mathrm{should}\: \\ $$$$\theta\:\mathrm{be}\:\mathrm{in}\:\mathrm{order}\:\mathrm{to}\:\mathrm{maximize}\:\mathrm{carrying}\:\mathrm{capasity} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{gutter}\:? \\ $$ Answered by EDWIN88 last updated…
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