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Category: Differentiation

y-1-x-2-dx-x-1-y-2-dy-0-

Question Number 112494 by bemath last updated on 08/Sep/20 $$\:\mathrm{y}\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:+\:\mathrm{x}\sqrt{\mathrm{1}+\mathrm{y}^{\mathrm{2}} }\:\mathrm{dy}\:=\:\mathrm{0} \\ $$ Answered by ajfour last updated on 08/Sep/20 $$\frac{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{{x}^{\mathrm{2}} }{d}\left({x}^{\mathrm{2}} \right)+\frac{\sqrt{\mathrm{1}+{y}^{\mathrm{2}}…

Question-46907

Question Number 46907 by Raj Singh last updated on 02/Nov/18 Answered by ajfour last updated on 02/Nov/18 $${y}=\left({x}^{\mathrm{2}} +\mathrm{3}\right)\left({x}^{\mathrm{3}} −\mathrm{5}\right) \\ $$$${y}+\bigtriangleup{y}=\left[\left({x}+\bigtriangleup{x}\right)^{\mathrm{2}} +\mathrm{3}\right]\left[\left({x}+\bigtriangleup{x}\right)^{\mathrm{3}} −\mathrm{5}\right] \\…

The-point-of-the-curve-3x-2-4y-2-72-which-nearest-to-the-line-3x-2y-1-is-a-6-3-c-6-6-b-6-3-d-6-5-

Question Number 112358 by john santu last updated on 07/Sep/20 $${The}\:{point}\:{of}\:{the}\:{curve}\:\mathrm{3}{x}^{\mathrm{2}} −\mathrm{4}{y}^{\mathrm{2}} =\mathrm{72} \\ $$$${which}\:{nearest}\:{to}\:{the}\:{line}\:\mathrm{3}{x}+\mathrm{2}{y}=\mathrm{1} \\ $$$${is\_\_\_} \\ $$$$\left({a}\right)\:\left(\mathrm{6},\mathrm{3}\right)\:\:\:\:\:\:\:\left({c}\right)\:\left(\mathrm{6},\mathrm{6}\right) \\ $$$$\left({b}\right)\:\left(\mathrm{6},−\mathrm{3}\right)\:\:\left({d}\right)\:\left(\mathrm{6},\mathrm{5}\right) \\ $$ Answered by…

1-n-m-N-Prove-that-3-m-n-10ln-m-n-6-mnH-m-H-n-H-m-i-1-m-1-i-H-n-j-1-n-1-j-

Question Number 46640 by canhtoan last updated on 29/Oct/18 $$\mathrm{1}\leqslant{n},{m}\in\mathbb{N}.\:{Prove}\:{that} \\ $$$$\mathrm{3}\left({m}+{n}\right)+\mathrm{10ln}\:\left({m}!{n}!\right)\geqslant\mathrm{6}\sqrt{{mnH}_{{m}} {H}_{{n}} }. \\ $$$$\left({H}_{{m}} =\underset{{i}=\mathrm{1}} {\overset{{m}} {\sum}}\frac{\mathrm{1}}{{i}},\:{H}_{{n}} =\underset{{j}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{j}}\right) \\ $$ Commented…

solution-of-0-1-xH-x-dx-x-1-0-1-x-x-1-dx-x-1-1-x-x-0-1-x-1-x-x-dx-2-1-0-1-x-d-dx-ln-x-2-1-xln-x-0-1-0-1-l

Question Number 112114 by mnjuly1970 last updated on 06/Sep/20 $$\:\:{solution}\:{of} \\ $$$$\Phi=\int_{\mathrm{0}} ^{\mathrm{1}} {xH}_{{x}} {dx}\:\overset{\gamma+\psi\left({x}+\mathrm{1}\right)} {=}\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}\left(\gamma+\psi\left({x}+\mathrm{1}\right)\right){dx}\: \\ $$$$\:\overset{\psi\left({x}+\mathrm{1}\right)=\frac{\mathrm{1}}{{x}}+\psi\left({x}\right)} {=}\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}\left(\gamma+\frac{\mathrm{1}}{{x}}+\psi\left({x}\right)\right){dx} \\ $$$$=\frac{\gamma}{\mathrm{2}}+\mathrm{1}+\:\int_{\mathrm{0}}…