Question Number 3324 by prakash jain last updated on 10/Dec/15 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{among}\:\mathrm{all}\:\mathrm{triangle}\:\mathrm{of}\:\mathrm{equal} \\ $$$$\mathrm{perimeter},\:\mathrm{equilateral}\:\mathrm{triangle}\:\mathrm{has}\:\mathrm{the} \\ $$$$\mathrm{largest}\:\mathrm{area}. \\ $$ Commented by 123456 last updated on 10/Dec/15 $$\mathrm{2}{s}\left({x},{y},{z}\right)={x}+{y}+{z}…
Question Number 134391 by bramlexs22 last updated on 03/Mar/21 $$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\int_{\mathrm{0}} ^{\:{x}} \:\left(\frac{{t}^{\mathrm{4}} −{t}^{\mathrm{2}} }{{t}^{\mathrm{2}} +\mathrm{1}}\right)\:{dt}. \\ $$$$\mathrm{Find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right). \\ $$ Answered by liberty last updated on…
Question Number 134373 by mnjuly1970 last updated on 02/Mar/21 Answered by Dwaipayan Shikari last updated on 02/Mar/21 $${I}\left({a}\right)=\underset{{n}=−\infty} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left({n}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)^{\mathrm{2}} }=\frac{\mathrm{1}}{{a}^{\mathrm{4}} }+\mathrm{2}\underset{{n}=\mathrm{1}} {\overset{\infty}…
Question Number 3228 by Rasheed Soomro last updated on 08/Dec/15 $$\mathcal{W}{hy}\:{is}\:{circumference}\:{of}\:{a}\:{circle}\:{derivative}\:{of} \\ $$$${its}\:{area}? \\ $$$$\frac{{d}}{{dr}}\left(\pi{r}^{\mathrm{2}} \right)=\mathrm{2}\pi{r}={circumference}. \\ $$ Commented by 123456 last updated on 08/Dec/15…
Question Number 134285 by bramlexs22 last updated on 02/Mar/21 $$\mathrm{Find}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt{\left(\mathrm{16}−\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{x}^{\mathrm{2}} −\mathrm{9}\right)}\: \\ $$ Answered by EDWIN88 last updated on 02/Mar/21 $$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)=\left(\mathrm{16}−\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{x}^{\mathrm{2}}…
Question Number 68703 by Maclaurin Stickker last updated on 15/Sep/19 $$\frac{{d}}{{dx}}\left({ln}\left(\sqrt{\frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}}\right)\right)=? \\ $$ Commented by MJS last updated on 15/Sep/19 $$\frac{{d}}{{dx}}\left[\mathrm{ln}\:\sqrt{\frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}}\right]=\frac{\mathrm{1}}{\mathrm{2}}×\frac{{d}}{{dx}}\left[\mathrm{ln}\:\frac{{x}^{\mathrm{2}}…
Question Number 134204 by liberty last updated on 01/Mar/21 $$\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt{\mathrm{2}\left(\mathrm{1}−\mathrm{cos}\:\mathrm{2x}\right)}\:. \\ $$$$\mathrm{find}\:\mathrm{f}\:'\left(\mathrm{0}\right). \\ $$ Answered by bramlexs22 last updated on 02/Mar/21 $$\:\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{2}\left(\mathrm{2sin}\:^{\mathrm{2}} \mathrm{x}\right)}\:=\mid\mathrm{4sin}\:\mathrm{x}\:\mid=\mathrm{2}\mid\mathrm{sin}\:\mathrm{x}\:\mid \\ $$$$\:\mathrm{f}\:'\left(\mathrm{0}^{−}…
Question Number 134127 by bobhans last updated on 28/Feb/21 $$\:\mathrm{Given}\:\mid\mathrm{f}\left(\mathrm{x}\right)\mid\:=\:\mathrm{x}^{\mathrm{2}} \:\mathrm{for}\:−\mathrm{1}<\mathrm{x}<\mathrm{1} \\ $$$$\mathrm{find}\:\mathrm{f}\:'\left(\mathrm{0}\right). \\ $$ Commented by EDWIN88 last updated on 28/Feb/21 $$\mathrm{does}\:\mathrm{not}\:\mathrm{exist} \\ $$…
Question Number 134108 by Eric002 last updated on 27/Feb/21 $$\frac{{d}}{{dx}}\left(\sqrt[{\mathrm{4}}]{\frac{{x}^{\mathrm{3}} +\mathrm{1}}{{x}^{\mathrm{3}} −\mathrm{1}}}\right) \\ $$ Answered by Ñï= last updated on 27/Feb/21 $$\frac{{d}}{{dx}}\left(\sqrt[{\mathrm{4}}]{\frac{{x}^{\mathrm{3}} +\mathrm{1}}{{x}^{\mathrm{3}} −\mathrm{1}}}\right) \\…
Question Number 134102 by mnjuly1970 last updated on 27/Feb/21 $$\:\:\:\:\:\:\:\:\:\:{prove}\:\:{that}\:: \\ $$$$\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{cos}\left(\sqrt{{x}}\:\right)}{{e}^{\mathrm{2}\pi\sqrt{{x}}\:} −\mathrm{1}}{dx}=\mathrm{1}−\frac{{e}}{\left({e}−\mathrm{1}\right)_{} ^{\mathrm{2}} } \\ $$ Answered by Dwaipayan Shikari last updated…