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Author: Tinku Tara

The-two-side-of-rectangle-are-2x-and-5-2x-units-respectively-For-what-value-of-x-the-area-of-rectangle-will-be-maximum-

Question Number 134874 by bemath last updated on 08/Mar/21 $$\mathrm{The}\:\mathrm{two}\:\mathrm{side}\:\mathrm{of}\:\mathrm{rectangle}\:\mathrm{are} \\ $$$$\mathrm{2}{x}\:\mathrm{and}\:\left(!\mathrm{5}−\mathrm{2}{x}\right)\:\mathrm{units}\:\mathrm{respectively} \\ $$$$\mathrm{For}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:{x}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of} \\ $$$$\mathrm{rectangle}\:\mathrm{will}\:\mathrm{be}\:\mathrm{maximum}? \\ $$ Commented by Ñï= last updated on 08/Mar/21…

prove-or-disprove-i-1-n-p-1-i-p-2-p-1-p-2-P-1-2-np-1-n-1-p-2-1-2-n-n-1-p-2-p-1-n-2-n-2-p-1-p-2-p-i-a-1-a-2-a-n-a-i-1-2-p-1-Z-p-1-0-n-Z-n-2-n-k-0-k-2-p-

Question Number 3794 by Filup last updated on 21/Dec/15 $$\mathrm{prove}\:\mathrm{or}\:\mathrm{disprove}:\:\:\:\:\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{p}_{\mathrm{1}} {i}={p}_{\mathrm{2}} \\ $$$${p}_{\mathrm{1}} ,{p}_{\mathrm{2}} \in\mathbb{P} \\ $$$$ \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{np}_{\mathrm{1}} \left({n}+\mathrm{1}\right)={p}_{\mathrm{2}} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{n}\left({n}+\mathrm{1}\right)=\frac{{p}_{\mathrm{2}} }{{p}_{\mathrm{1}}…

f-x-y-f-x-1-y-y-x-gt-0-f-x-y-y-1-x-x-0-y-gt-0-xy-x-0-y-0-f-5-7-f-6-9-

Question Number 3793 by 123456 last updated on 21/Dec/15 $${f}\left({x},{y}\right)=\begin{cases}{{f}\left({x}−\mathrm{1},{y}\right)+{y}}&{{x}>\mathrm{0}}\\{{f}\left({x}+{y},{y}−\mathrm{1}\right)+{x}}&{{x}\leqslant\mathrm{0}\wedge{y}>\mathrm{0}}\\{{xy}}&{{x}\leqslant\mathrm{0}\wedge{y}\leqslant\mathrm{0}}\end{cases} \\ $$$${f}\left(\mathrm{5},\mathrm{7}\right)=? \\ $$$${f}\left(\mathrm{6},\mathrm{9}\right)=?? \\ $$ Commented by prakash jain last updated on 21/Dec/15 $${y}>\mathrm{0}…

let-U-n-0-cos-nx-x-2-n-2-2-dx-calculate-lim-n-e-n-2-U-n-

Question Number 134866 by mathmax by abdo last updated on 07/Mar/21 $$\mathrm{let}\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{cos}\left(\mathrm{nx}\right)}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{n}^{\mathrm{2}} \right)^{\mathrm{2}} }\mathrm{dx}\:\mathrm{calculate}\:\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \mathrm{e}^{\mathrm{n}^{\mathrm{2}} } \mathrm{U}_{\mathrm{n}} \\ $$ Answered by…

f-nx-f-x-n-f-x-f-0-0-f-x-

Question Number 3789 by 123456 last updated on 21/Dec/15 $${f}\left({nx}\right)={f}\left({x}+{n}\right)−{f}\left({x}\right) \\ $$$${f}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$${f}\left({x}\right)=? \\ $$ Commented by Rasheed Soomro last updated on 21/Dec/15 $${f}\left({nx}\right)={f}\left({x}+{n}\right)−{f}\left({x}\right)…

Question-134858

Question Number 134858 by mnjuly1970 last updated on 07/Mar/21 Answered by mathmax by abdo last updated on 07/Mar/21 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{lnxln}^{\mathrm{2}} \left(\mathrm{1}−\mathrm{x}\right)\:\mathrm{changement}\:\mathrm{1}−\mathrm{x}=\mathrm{t}\:\mathrm{give}\:\mathrm{x}=\mathrm{1}−\mathrm{t}\:\:\left(\mathrm{t}\rightarrow\mathrm{0}^{+} \right) \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{ln}\left(\mathrm{1}−\mathrm{t}\right)\mathrm{ln}^{\mathrm{2}} \left(\mathrm{t}\right)\:=\mathrm{g}\left(\mathrm{t}\right)\:\mathrm{we}\:\mathrm{have} \\…

nice-calculus-find-0-1-ln-x-ln-1-x-x-1-x-dx-

Question Number 134852 by mnjuly1970 last updated on 07/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:\:\:{calculus}… \\ $$$$\:\:\:\:\:\:{find}\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left({x}\right){ln}\left(\mathrm{1}−{x}\right)}{{x}\left(\mathrm{1}−{x}\right)}{dx}=? \\ $$$$ \\ $$ Answered by mnjuly1970 last updated…