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Author: Tinku Tara

find-C-z-2-sin-z-2-dz-z-3pi-

Question Number 147406 by tabata last updated on 20/Jul/21 $${find}\:\int_{{C}} \frac{{z}+\mathrm{2}}{{sin}\left(\frac{{z}}{\mathrm{2}}\right)}{dz}\:\:\:,\mid{z}\mid=\mathrm{3}\pi \\ $$ Answered by Olaf_Thorendsen last updated on 20/Jul/21 $$\Omega\:=\:\int_{\mid{z}\mid=\mathrm{3}\pi} \frac{{z}+\mathrm{2}}{\mathrm{sin}\left(\frac{{z}}{\mathrm{2}}\right)}\:{dz} \\ $$$$\Omega\:=\:\int_{\mid{z}\mid=\mathrm{3}\pi} \frac{{z}+\mathrm{2}}{{z}}×\frac{{z}}{\mathrm{sin}\left(\frac{{z}}{\mathrm{2}}\right)}\:{dz}…

f-x-1-x-2-x-2018-f-0-

Question Number 147402 by vvvv last updated on 20/Jul/21 $$\boldsymbol{{f}}\left(\boldsymbol{{x}}+\mathrm{1}\right)\left(\boldsymbol{{x}}+\mathrm{2}\right)….\left(\boldsymbol{{x}}+\mathrm{2018}\right) \\ $$$$\boldsymbol{{f}}'\left(\mathrm{0}\right)=? \\ $$ Answered by SEKRET last updated on 21/Jul/21 $$\:\:\boldsymbol{\mathrm{y}}=\left(\boldsymbol{\mathrm{x}}+\mathrm{1}\right)\left(\boldsymbol{\mathrm{x}}+\mathrm{2}\right)\centerdot….\left(\boldsymbol{\mathrm{x}}+\mathrm{2018}\right) \\ $$$$\:\:\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{y}}\right)\:=\:\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}+\mathrm{1}\right)+\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}+\mathrm{2}\right)+..+\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}+\mathrm{2018}\right) \\…