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Author: Tinku Tara

Let-f-and-g-be-functions-such-that-for-all-real-number-x-and-y-g-f-x-y-f-x-x-y-g-y-Find-the-value-of-g-0-g-1-g-2-g-3-g-2016-

Question Number 4702 by 314159 last updated on 22/Feb/16 $$\mathrm{Let}\:\mathrm{f}\:\mathrm{and}\:\mathrm{g}\:\mathrm{be}\:\mathrm{functions}\:\mathrm{such}\:\mathrm{that}\:\mathrm{for}\:\mathrm{all} \\ $$$$\mathrm{real}\:\mathrm{number}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y},\mathrm{g}\left(\mathrm{f}\left(\mathrm{x}+\mathrm{y}\right)\right)=\mathrm{f}\left(\mathrm{x}\right)+\left(\mathrm{x}+\mathrm{y}\right)\mathrm{g}\left(\mathrm{y}\right). \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{g}\left(\mathrm{0}\right)+\mathrm{g}\left(\mathrm{1}\right)+\mathrm{g}\left(\mathrm{2}\right)+\mathrm{g}\left(\mathrm{3}\right)+…+\mathrm{g}\left(\mathrm{2016}\right). \\ $$ Commented by prakash jain last updated on 22/Feb/16 $$\mathrm{Let}\:\mathrm{us}\:\mathrm{try}\:\mathrm{for}\:\mathrm{trivial}\:\mathrm{solution}…

Solve-xy-y-sin-x-y-5-0-

Question Number 70232 by Joel122 last updated on 02/Oct/19 $$\mathrm{Solve} \\ $$$${xy}'\:−\:{y}\:\mathrm{sin}\:{x}\:+\:{y}^{\mathrm{5}} \:=\:\mathrm{0} \\ $$ Commented by Joel122 last updated on 02/Oct/19 $$\mathrm{I}\:\mathrm{think}\:\mathrm{it}\:\mathrm{is}\:\mathrm{a}\:\mathrm{Bernoulli}'\mathrm{s}\:\mathrm{equation} \\ $$$${y}'\:−\:\left(\frac{\mathrm{sin}\:{x}}{{x}}\right){y}\:=\:−\frac{{y}^{\mathrm{5}}…

Question-70225

Question Number 70225 by TawaTawa last updated on 02/Oct/19 Commented by TawaTawa last updated on 02/Oct/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\:\mathrm{A}\left(\mathrm{ECD}\right)\:−\:\mathrm{A}\left(\mathrm{BAE}\right)\:\:\mathrm{in}\:\mathrm{cm}^{\mathrm{2}} \\ $$ Commented by MJS last updated on…

1-1-2-1-1-2-1-2-2-1-1-2-1-3-2-2-3-1-1-2-1-3-1-4-3-2-4-1-1-2-1-3-1-4-1-5-5-2-5-

Question Number 135757 by Dwaipayan Shikari last updated on 15/Mar/21 $$\frac{\mathrm{1}.\mathrm{1}}{\mathrm{2}}+\frac{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+\frac{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}\right)\mathrm{2}}{\mathrm{2}^{\mathrm{3}} }+\frac{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}\right)\mathrm{3}}{\mathrm{2}^{\mathrm{4}} }+\frac{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{5}}\right)\mathrm{5}}{\mathrm{2}^{\mathrm{5}} }+… \\ $$ Commented by Dwaipayan Shikari last updated on 15/Mar/21…