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Author: Tinku Tara

y-2y-sin-x-2y-3-2-sin-x-

Question Number 128420 by bramlexs22 last updated on 07/Jan/21 $$\:\mathrm{y}'=\mathrm{2y}\:\mathrm{sin}\:\mathrm{x}\:−\mathrm{2y}^{\mathrm{3}/\mathrm{2}} \:\mathrm{sin}\:\mathrm{x}\: \\ $$ Answered by liberty last updated on 07/Jan/21 $$\mathrm{y}'=\mathrm{2sin}\:\mathrm{x}\left(\mathrm{y}−\mathrm{y}^{\mathrm{3}/\mathrm{2}} \right) \\ $$$$\frac{\mathrm{dy}}{\mathrm{y}−\mathrm{y}^{\mathrm{3}/\mathrm{2}} }\:=\:\mathrm{2sin}\:\mathrm{x}\:\mathrm{dx}\:…

let-f-x-ln-x-1-x-1-1-determine-D-f-2-calculatef-n-x-and-f-n-0-3-developp-f-at-integr-serie-4-calculate-1-2-1-2-f-x-dx-

Question Number 62882 by mathmax by abdo last updated on 26/Jun/19 $${let}\:{f}\left({x}\right)={ln}\mid\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}\mid \\ $$$$\left.\mathrm{1}\right){determine}\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right)\:{calculatef}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{−\frac{\mathrm{1}}{\mathrm{2}}} ^{\frac{\mathrm{1}}{\mathrm{2}}} {f}\left({x}\right){dx}\:. \\…

If-lim-x-0-ln-a-x-ln-a-x-k-lim-x-e-ln-x-1-x-e-1-then-k-

Question Number 128411 by bramlexs22 last updated on 07/Jan/21 $$\:\mathrm{If}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{ln}\:\left({a}+{x}\right)−\mathrm{ln}\:{a}}{{x}}\right)+\:{k}\:\underset{{x}\rightarrow\mathrm{e}} {\mathrm{lim}}\left(\frac{\mathrm{ln}\:{x}−\mathrm{1}}{{x}−{e}}\right)=\mathrm{1} \\ $$$$\mathrm{then}\:{k}\:=\: \\ $$ Answered by Dwaipayan Shikari last updated on 07/Jan/21 $$\underset{{x}\rightarrow\mathrm{0}}…