Question Number 75222 by chess1 last updated on 08/Dec/19 Commented by chess1 last updated on 09/Dec/19 $$\mathrm{Sir}\:\boldsymbol{\mathrm{W}}\:\:\:\mathrm{solution}\:\mathrm{please} \\ $$ Terms of Service Privacy Policy Contact:…
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Question Number 9686 by tawakalitu last updated on 24/Dec/16 Answered by mrW last updated on 24/Dec/16 $$\mathrm{u}=\mathrm{log}\:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} \right) \\ $$$$\frac{\mathrm{du}}{\mathrm{dy}}=\frac{\mathrm{2y}}{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} }×\mathrm{log}\:\mathrm{e}…
Question Number 75220 by ~blr237~ last updated on 08/Dec/19 $$\mathrm{Let}\:\mathrm{us}\:\mathrm{consider}\:\mathrm{the}\:\mathrm{function}\: \\ $$$$\mathrm{F}\left(\mathrm{x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{e}^{−\mathrm{x}} \mathrm{ln}\left(\mathrm{x}−\mathrm{lnt}\right)\mathrm{dt}\: \\ $$$$\left.\mathrm{1}\right)\mathrm{Prove}\:\mathrm{that}\:\mathrm{for}\:\mathrm{all}\:\mathrm{x}\geqslant\mathrm{1}\:,\:\:\mathrm{F}\left(\mathrm{x}\right)\:\mathrm{exist} \\ $$$$\left.\mathrm{2}\right)\mathrm{Prove}\:\mathrm{that}\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{tln}\left(\mathrm{x}−\mathrm{lnt}\right)=\mathrm{0} \\ $$$$\left.\mathrm{3}\right)\mathrm{Prove}\:\mathrm{that}\:\mathrm{F}\:\in\:\mathrm{C}^{\mathrm{1}} \left(\left[\mathrm{1}:\infty\left[,\left[\mathrm{1}:\infty\left[\right)\:\mathrm{and}\:\mathrm{for}\:\right.\right.\right.\right. \\ $$$$\mathrm{all}\:\mathrm{x}\geqslant\mathrm{1}\:\:\mathrm{F}\left(\mathrm{x}\right)=\mathrm{F}'\left(\mathrm{x}\right)+\mathrm{lnx}…
Question Number 75218 by 21042004 last updated on 08/Dec/19 $$\mathrm{Simplify}:\:\left({x}^{\mathrm{4}} −\mathrm{3}{x}^{\mathrm{3}} +\mathrm{4}{x}^{\mathrm{2}} −\mathrm{12}{x}\right)\::\:\left({x}^{\mathrm{2}} +\mathrm{4}\right) \\ $$ Commented by JDamian last updated on 08/Dec/19 $${That}\:{is}\:{not}\:{a}\:{equation} \\…
Question Number 9683 by tawakalitu last updated on 23/Dec/16 Commented by geovane10math last updated on 25/Dec/16 $$\mathrm{I}'\mathrm{m}\:\mathrm{working}\:\mathrm{in}\:\mathrm{this}\:\mathrm{problem}. \\ $$$$ \\ $$ Commented by geovane10math last…
Question Number 140749 by SOMEDAVONG last updated on 12/May/21 $$\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{5}^{\frac{\mathrm{1}}{\mathrm{k}}} \left(\mathrm{1}−\mathrm{5}^{−\frac{\mathrm{1}}{\mathrm{k}\left(\mathrm{k}+\mathrm{1}\right)}} \right)=? \\ $$ Answered by Dwaipayan Shikari last updated on 12/May/21 $$\mathrm{5}^{\frac{\mathrm{1}}{{k}}}…
Question Number 140748 by 676597498 last updated on 12/May/21 Answered by qaz last updated on 12/May/21 $$\left({i}\right)…{r}=\frac{\mathrm{2}}{\mathrm{1}+\mathrm{sin}\:\theta} \\ $$$$\Rightarrow{r}+{r}\mathrm{sin}\:\theta=\mathrm{2} \\ $$$$\Rightarrow\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }+{y}=\mathrm{2} \\ $$$$\Rightarrow{x}^{\mathrm{2}}…
Question Number 9678 by ridwan balatif last updated on 23/Dec/16 Commented by ridwan balatif last updated on 23/Dec/16 $$\mathrm{let}\:\mathrm{x}\:\:\mathrm{and}\:\mathrm{y}\:\mathrm{is}\:\mathrm{real}\:\mathrm{number}\:\mathrm{that}\:\mathrm{x}+\mathrm{y}=\mathrm{2}.\:\mathrm{If} \\ $$$$\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\sqrt{\mathrm{16}+\mathrm{3x}^{\mathrm{2}} }+\mathrm{2}\sqrt{\mathrm{73}+\mathrm{3y}^{\mathrm{2}} }=\mathrm{m} \\ $$$$\mathrm{find}\:\mathrm{value}\:\mathrm{of}\:\mathrm{m}^{\mathrm{2}}…
Question Number 140751 by peter frank last updated on 12/May/21 Answered by Ar Brandon last updated on 12/May/21 $$\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{n}} =\underset{\mathrm{r}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{r}} \mathrm{x}^{\mathrm{r}} \\…