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Category: Differentiation

find-max-and-min-value-of-f-x-y-4x-2-8xy-9y-2-8x-24y-4-

Question Number 119240 by benjo_mathlover last updated on 23/Oct/20 $${find}\:{max}\:{and}\:{min}\:{value}\:{of}\: \\ $$$${f}\left({x},{y}\right)\:=\:\mathrm{4}{x}^{\mathrm{2}} +\mathrm{8}{xy}+\mathrm{9}{y}^{\mathrm{2}} −\mathrm{8}{x}−\mathrm{24}{y}+\mathrm{4}\: \\ $$ Answered by 1549442205PVT last updated on 23/Oct/20 $${f}\left({x},{y}\right)\:=\:\mathrm{4}{x}^{\mathrm{2}} +\mathrm{8}{xy}+\mathrm{9}{y}^{\mathrm{2}}…

Given-f-x-sin-x-cos-x-sin-x-cos-x-find-the-value-of-f-x-f-x-1-

Question Number 118969 by benjo_mathlover last updated on 21/Oct/20 $$\:{Given}\:{f}\left({x}\right)\:=\:\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}−\mathrm{cos}\:{x}} \\ $$$${find}\:{the}\:{value}\:{of}\: \\ $$$$\:{f}\:''\left({x}\right)\:+\:{f}\:'\left({x}\right)\:+\:\mathrm{1}\:. \\ $$ Answered by TANMAY PANACEA last updated on 21/Oct/20 $${f}\left({x}\right)=\frac{{tanx}+\mathrm{1}}{{tanx}−\mathrm{1}}=−{tan}\left(\frac{\pi}{\mathrm{4}}+{x}\right)…

The-general-solution-of-the-equation-dy-dx-ylnx-x-x-a-x-x-1-ce-x-b-x-x-1-ce-2x-c-x-x-1-ce-x-

Question Number 53426 by Necxx last updated on 21/Jan/19 $${The}\:{general}\:{solution}\:{of}\:{the}\:{equation} \\ $$$$\frac{{dy}}{{dx}}+{ylnx}={x}^{−{x}} \\ $$$$\left.{a}\left.\right){x}^{{x}} \left(\mathrm{1}−{ce}^{{x}} \right)\:\:{b}\right)−{x}^{−{x}} \left(\mathrm{1}+{ce}^{\mathrm{2}{x}} \right) \\ $$$$\left.{c}\right)−{x}^{−{x}} \left(\mathrm{1}−{ce}^{{x}} \right) \\ $$ Commented…

Question-118887

Question Number 118887 by rexfordattacudjoe last updated on 20/Oct/20 Answered by benjo_mathlover last updated on 20/Oct/20 $$\:{f}\:'\left({x}\right)\:=\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{{x}+{h}}\:−\sqrt{{x}}}{{h}} \\ $$$$\:=\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}+{h}−{x}}{{h}}\:×\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{\:\sqrt{{x}+{h}}\:+\:\sqrt{{x}}\:} \\ $$$$=\:\mathrm{1}×\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}\:=\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}} \\…