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Category: Differentiation

let-f-x-y-x-2-y-2-sin-1-x-2-y-2-if-x-y-0-0-and-f-0-0-0-prove-that-f-is-differenciable-at-all-point-of-R-2-2-prove-that-f-x-and-f-y-are-not-differdnciable-at-0-0-

Question Number 36176 by prof Abdo imad last updated on 30/May/18 $${let}\:{f}\left({x},{y}\right)\:=\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right){sin}\left\{\:\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }}\right\}\:{if}\left({x},{y}\right)=\left(\mathrm{0},\mathrm{0}\right) \\ $$$${and}\:{f}\left(\mathrm{0},\mathrm{0}\right)=\mathrm{0} \\ $$$${prove}\:{that}\:{f}\:{is}\:{differenciable}\:{at}\:{all}\:{point}\:{of}\:{R}^{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\frac{\partial{f}}{\partial{x}}\:{and}\:\frac{\partial{f}}{\partial{y}}\:{are}\:{not}\:{differdnciable} \\ $$$${at}\:\left(\mathrm{0},\mathrm{0}\right) \\…

calculate-f-x-and-f-y-in-this-cases-1-f-x-y-e-x-sin-2y-1-2-f-x-y-x-2-y-2-e-xy-3-f-x-y-x-x-2-y-2-

Question Number 36173 by prof Abdo imad last updated on 30/May/18 $${calculate}\:\frac{\partial{f}}{\partial{x}}\:{and}\:\frac{\partial{f}}{\partial{y}}\:{in}\:{this}\:{cases} \\ $$$$\left.\mathrm{1}\right)\:{f}\left({x},{y}\right)=\:{e}^{−{x}} \:{sin}\left(\mathrm{2}{y}\:+\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right){f}\left({x},{y}\right)\:=\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right){e}^{−{xy}} \\ $$$$\left.\mathrm{3}\right){f}\left({x},{y}\right)\:=\:\frac{{x}}{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} } \\ $$…

lim-0-sin-x-dx-pi-2-0-sin-x-dx-x-y-1-0-sin-y-y-1-1-dy-0-sin-x-

Question Number 167230 by mnjuly1970 last updated on 10/Mar/22 $$ \\ $$$$\:\:\:\:\:{lim}_{\:\alpha\rightarrow\infty} \left\{\:\left(\alpha\:\int_{\mathrm{0}} ^{\:\infty} {sin}\left(\:{x}^{\:\alpha} \right)\:{dx}\:\right)=\varphi\left(\alpha\right)\right]=\:\frac{\pi}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:−−−− \\ $$$$\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} {sin}\left({x}^{\:\alpha} \right){dx}\:\overset{{x}^{\:\alpha} =\:{y}} {=}\:\frac{\mathrm{1}}{\alpha}\int_{\mathrm{0}}…

Find-minimum-value-of-function-f-x-2x-x-1-x-2-1-

Question Number 167167 by cortano1 last updated on 08/Mar/22 $$\:\:\mathrm{Find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{function}\: \\ $$$$\:\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2x}−\sqrt{\mathrm{x}+\mathrm{1}}−\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}} \\ $$ Answered by MJS_new last updated on 08/Mar/22 $${f}\left(−\mathrm{1}\right)=−\mathrm{2} \\ $$$${f}\:\mathrm{has}\:\mathrm{a}\:\mathrm{singularity}\:\mathrm{at}\:{x}=−\mathrm{1}…

Question-167158

Question Number 167158 by mnjuly1970 last updated on 08/Mar/22 Answered by mindispower last updated on 10/Mar/22 $${cos}\left(\mathrm{3}{n}\right)=\mathrm{4}{cos}^{\mathrm{3}} \left({n}\right)−\mathrm{3}{cos}\left({n}\right)\Rightarrow{cos}^{\mathrm{3}} \left({n}\right)=\frac{{cos}\left(\mathrm{3}{n}\right)+\mathrm{3}{cos}\left({n}\right)}{\mathrm{4}} \\ $$$$\Theta=\frac{\mathrm{1}}{\mathrm{4}}{Re}\left\{\underset{{n}\geqslant\mathrm{1}} {\sum}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{n}^{\mathrm{2}} }.\left({e}^{\mathrm{3}{in}} +\mathrm{3}{e}^{{in}}…

if-y-sin2x-is-the-solution-of-differintial-equation-d-2-y-dx-2-4y-k-then-the-k-is-

Question Number 101558 by mhmd last updated on 03/Jul/20 $${if}\:{y}={sin}\mathrm{2}{x}\:{is}\:{the}\:{solution}\:{of}\:{differintial}\:{equation}\: \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\mathrm{4}{y}={k}\:{then}\:{the}\:{k}\:{is}\:……. \\ $$ Answered by bemath last updated on 03/Jul/20 $$\mathrm{y}'=\mathrm{2cos}\:\mathrm{2x}\:\Rightarrow\mathrm{y}''=−\mathrm{4sin}\:\mathrm{2x} \\…