Category: Differentiation

Question Number 146164 by mnjuly1970 last updated on 11/Jul/21 $$$$$$calulate::$$$$\mathrm{S}:=\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{{\mathrm{H}}_{\frac{n}{2}}}{2^n}=?$$$$$$$$\dots \dots .m.n.$$ Answered…

Question Number 146054 by mnjuly1970 last updated on 10/Jul/21 $$$$$$\mathrm{I}:={\int }_0^{\mathrm{\infty }}{e}^{-x}.{\mathrm{J}}_{\frac{1}{2}}\left(x\right)dx$$$$\:\:\:\:\:\:\:\:\:\:\mathrm{J}_{{v}\:} \:\left({x}\:\right)\:=\:{x}^{\:{v}} \:\underset{{n}=\mathrm{0}} {\overset{\:\infty} {\sum}}\frac{\left(−\:\mathrm{1}\:\right)^{\:{n}} \:{x}^{\:\mathrm{2}{n}} }{\mathrm{2}^{\:{n}\:+\:{v}} \:{n}\:!\:\Gamma\:\left(\:{n}\:+\:{v}\:+\mathrm{1}\:\right)}…

Question Number 145701 by alcohol last updated on 07/Jul/21 Commented by MJS_new last updated on 07/Jul/21 $$1.$$$$\mathrm{square}-2\times (\mathrm{square}-\mathrm{quarter}\mathrm{circle})=$$$$=-\mathrm{square}+2\times \mathrm{quarter}\mathrm{circle}=$$$$=\mathrm{half}\:\mathrm{circle}−\mathrm{square}=\mathrm{4}^{\mathrm{2}} \pi/\mathrm{2}−\mathrm{4}^{\mathrm{2}} =…

Question Number 145602 by mnjuly1970 last updated on 06/Jul/21 $$$$$$\dots ..\mathrm{Advanced}\dots \dots \dots \mathrm{Calculus}\dots ..$$$$\mathrm{Q}::\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}::$$$$$$$$\overline{)\begin{array}{c}i::\mathit{\varphi }:={\int }_0^1\mathrm{Ln}\left(\mathrm{\Gamma }(2+x)\right)dx=?\\ ii::\mathrm{\Omega }:=\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{1}{n(2n+3)}=?\end{array}}$$$$ \…

Question Number 80027 by jagoll last updated on 30/Jan/20 $$findminimum$$$$valueof\sqrt{x^2+4}+\sqrt{x^2-24x+153}$$$$forx⩾0in\mathbb{R}$$ Commented by john santu last updated on…