Question Number 148645 by metamorfose last updated on 29/Jul/21 $${u}_{{n}+\mathrm{3}} =\frac{{u}_{{n}+\mathrm{2}} +{u}_{{n}+\mathrm{1}} +{u}_{{n}} }{\mathrm{3}}\:,\:\forall{n}\in{IN} \\ $$$${find}\:{u}_{{n}} \: \\ $$ Answered by Olaf_Thorendsen last updated on…
Question Number 83110 by 09658867628 last updated on 28/Feb/20 $${bounded}\:{by}\:{the}\:{curve}\:{y}=\sqrt{\mathrm{4}-{x}}\:{y}=\mathrm{0}\:{y}=\mathrm{1} \\ $$ Commented by jagoll last updated on 28/Feb/20 $$\mathrm{Area}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{4}−\mathrm{y}^{\mathrm{2}} \right)\:\mathrm{dy}\: \\ $$$$=\:\mathrm{4y}\:−\:\frac{\mathrm{y}^{\mathrm{3}}…
Question Number 17575 by tawa tawa last updated on 07/Jul/17 Commented by tawa tawa last updated on 08/Jul/17 $$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}.\:\mathrm{Any}\:\mathrm{mathematical}\:\mathrm{prove}\:??? \\ $$ Commented by prakash jain…
Question Number 83108 by M±th+et£s last updated on 28/Feb/20 $${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{{cos}\left({nx}\right)}{{cos}^{{n}} \left({x}\right)}\:{dx}\:=\mathrm{2}^{{n}} \left[\frac{\pi}{\mathrm{8}}−\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\sum}}\frac{{sin}\left(\frac{{k}\pi}{\mathrm{4}}\right)}{\mathrm{2}{k}\left(\sqrt{\mathrm{2}}\right)^{{k}} }\right]\:{n}\in{N}^{\ast} \\ $$ Answered by mind is…
Question Number 83109 by 09658867628 last updated on 28/Feb/20 $$\int_{\mathrm{1}/\boldsymbol{{e}}} ^{{e}} \frac{\boldsymbol{{dt}}}{\boldsymbol{{t}}} \\ $$ Commented by jagoll last updated on 28/Feb/20 $$=\:\mathrm{ln}\:\left(\mathrm{t}\right)\:\mid_{\frac{\mathrm{1}}{\mathrm{e}}} ^{\mathrm{e}} \:=\:\mathrm{1}−\left(−\mathrm{1}\right)\:=\:\mathrm{2} \\…
Question Number 83104 by 09658867628 last updated on 28/Feb/20 $$\int\frac{{e}^{{x}} {dx}}{\mathrm{3}+{e}^{{x}} } \\ $$ Answered by MJS last updated on 28/Feb/20 $$\int\frac{\mathrm{e}^{{x}} }{\mathrm{3}+\mathrm{e}^{{x}} }{dx}= \\…
Question Number 83102 by ajfour last updated on 28/Feb/20 Commented by ajfour last updated on 28/Feb/20 $$\mathrm{Find}\:\mathrm{side}\:\boldsymbol{\mathrm{s}}\:\mathrm{of}\:\mathrm{largest}\:\mathrm{equilateral} \\ $$$$\bigtriangleup\mathrm{ABC}\:\mathrm{whose}\:\mathrm{vertices}\:\mathrm{lie}\:\mathrm{on} \\ $$$$\mathrm{three}\:\mathrm{circles}\:\mathrm{of}\:\mathrm{radii}\:\mathrm{p},\mathrm{q},\mathrm{r}\:\mathrm{touching} \\ $$$$\mathrm{each}\:\mathrm{other}\:\mathrm{externally}. \\ $$…
Question Number 148636 by tabata last updated on 29/Jul/21 $${find}\:{tylor}\:{series}\:{of}\:{f}\left({z}\right)={logz}\: \\ $$$${about}\:{z}_{{o}} =−\mathrm{1}+{i} \\ $$ Commented by tabata last updated on 29/Jul/21 $$???? \\ $$…
Question Number 148639 by tabata last updated on 29/Jul/21 $${find}\:{singular}\:{point}\:{of}\:{this}\:{following}\:{and} \\ $$$${whats}\:{the}\:{type}\:{of}\:{singular}\:{point}\:? \\ $$$$ \\ $$$$\left(\mathrm{1}\right){f}\left({z}\right)=\frac{\mathrm{1}}{{lnz}} \\ $$$$ \\ $$$$\left(\mathrm{2}\right){f}\left({z}\right)=\frac{\mathrm{1}−{cos}\left({z}+{i}\right)}{{z}\left({z}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$ \\…
Question Number 148638 by tabata last updated on 29/Jul/21 $${find}\:{laurent}\:{series}\:{f}\left({z}\right)=\frac{{cos}\left({iz}\right)}{{z}^{{n}} }\:\:,\mid{z}−{i}\mid>\mathrm{2} \\ $$ Commented by tabata last updated on 29/Jul/21 $$???? \\ $$ Terms of…