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Author: Tinku Tara

Help-me-complex-anaylsis-problem-f-z-is-entire-in-path-C-entire-Differantiable-complex-function-mean-f-z-satisfy-f-z-u-x-y-i-v-x-y-u-x-v-y-or-u-y-v-x-couch

Question Number 213862 by issac last updated on 19/Nov/24 $$\mathrm{Help}\:\mathrm{me}…..!!!\:\::\left(\:\:\right. \\ $$$$\mathrm{complex}\:\mathrm{anaylsis}\:\mathrm{problem}.. \\ $$$${f}\left({z}\right)\:\mathrm{is}\:\mathrm{entire}\:\mathrm{in}\:\mathrm{path}\:{C}\: \\ $$$$\mathrm{entire}:\:\mathrm{Differantiable}\:\mathrm{complex}\:\mathrm{function} \\ $$$$\mathrm{mean}\:{f}\left({z}\right)\:\mathrm{satisfy}\:{f}\left({z}\right)={u}\left({x},{y}\right)+\boldsymbol{{i}}\centerdot{v}\left({x},{y}\right)\:\: \\ $$$$\frac{\partial{u}}{\partial{x}}=−\frac{\partial{v}}{\partial{y}}\:\mathrm{or}\:\:\frac{\partial{u}}{\partial{y}}=−\frac{\partial{v}}{\partial{x}}\:\left(\mathrm{couchy}-\mathrm{riemann}\right) \\ $$$$\mathrm{show}\:\mathrm{that}\:\int_{\:{C}} \:\frac{{f}\left({z}\right)}{{f}'\left({z}\right)}\:\mathrm{d}{z}=\mathrm{2}\pi\boldsymbol{{i}}\underset{{h}=\mathrm{1}} {\overset{{M}} {\sum}}\:{P}_{{h}}…

Question-213838

Question Number 213838 by ajfour last updated on 18/Nov/24 Commented by ajfour last updated on 18/Nov/24 $${A}\:{solid}\:{ball}\:{is}\:{released}\:{over}\:{a}\:{fixed} \\ $$$${cylindrical}\:{wedge}\:{as}\:{shown}.\:{Friction} \\ $$$${is}\:{sufficient}.\:{If}\:{just}\:{after}\:{the}\:{ball} \\ $$$${leaves}\:{the}\:{curved}\:{surface}\:{due}\:{to} \\ $$$${Normal}\:{reaction}\:{vanishing},\:{it}\:…

Question-213835

Question Number 213835 by BaliramKumar last updated on 18/Nov/24 Answered by mehdee7396 last updated on 18/Nov/24 $${OA}=\sqrt{\mathrm{13}}\:\:\&\:\:\:{OB}=\mathrm{3} \\ $$$${sin}\frac{\theta}{\mathrm{2}}=\frac{\mathrm{3}}{\:\sqrt{\mathrm{13}}}\Rightarrow{cos}\frac{\theta}{\mathrm{2}}=\frac{\mathrm{2}}{\:\sqrt{\mathrm{13}}} \\ $$$$\Rightarrow{tan}\frac{\theta}{\mathrm{2}}=\frac{\mathrm{3}}{\mathrm{2}}\Rightarrow\theta=\mathrm{2}{tan}^{−\mathrm{1}} \frac{\mathrm{3}}{\mathrm{2}}\:\:\checkmark \\ $$$$ \\…

path-C-is-closed-f-is-regular-function-in-Path-C-f-is-have-zero-point-and-poles-in-C-show-that-C-f-z-f-z-dz-2pii-Z-P-and-if-poles-are-not-exist-show-that-C-f-z-f-z-dz-2

Question Number 213846 by issac last updated on 18/Nov/24 $$\mathrm{path}\:\mathscr{C}\:\mathrm{is}\:\mathrm{closed} \\ $$$${f}\:\mathrm{is}\:\mathrm{regular}\:\mathrm{function}\:\mathrm{in}\:\mathrm{Path}\:\mathscr{C} \\ $$$${f}\:\mathrm{is}\:\mathrm{have}\:\mathrm{zero}\:\mathrm{point}\:\mathrm{and}\:\mathrm{poles}\:\mathrm{in}\:\mathscr{C} \\ $$$$\mathrm{show}\:\mathrm{that}\: \\ $$$$\oint_{\:\mathscr{C}} \:\frac{{f}\left({z}\right)}{{f}'\left({z}\right)}\:\mathrm{d}{z}=\mathrm{2}\pi\boldsymbol{{i}}\left({Z}−{P}\right) \\ $$$$\mathrm{and}\:\mathrm{if}\:\mathrm{poles}\:\mathrm{are}\:\mathrm{not}\:\mathrm{exist} \\ $$$$\mathrm{show}\:\mathrm{that} \\ $$$$\oint_{\:\mathscr{C}\:}…

Find-the-vertical-asymptots-of-f-x-tan-pi-2x-2-in-0-4-

Question Number 213841 by mnjuly1970 last updated on 18/Nov/24 $$ \\ $$$$\:\:{Find}\:{the}\:{vertical}\:{asymptots} \\ $$$$\: \\ $$$$\:\:{of}\:\:,\:\:\:{f}\left({x}\right)=\:\mathrm{tan}\left(\frac{\:\pi}{\mathrm{2}{x}\:+\:\mathrm{2}}\:\right)\:\:{in}\: \\ $$$$\: \\ $$$$\:\:\:\:\:\left[\:\mathrm{0}\:\:,\:\:\:\mathrm{4}\:\right] \\ $$$$\:−−−−−−−−−−−−− \\ $$$$ \\…

Find-lim-x-0-sinx-x-sinx-x-sinx-

Question Number 213821 by hardmath last updated on 17/Nov/24 $$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{sinx}}{\mathrm{x}}\right)^{\frac{\mathrm{sinx}}{\mathrm{x}\:−\:\mathrm{sinx}}} \:\:=\:\:? \\ $$ Answered by mehdee7396 last updated on 17/Nov/24 $${lim}_{{x}\rightarrow\mathrm{0}} \left(\frac{{sinx}}{{x}}−\mathrm{1}\right)\frac{{sinx}}{{x}−{sinx}} \\ $$$$={lim}_{{x}\rightarrow\mathrm{0}}…