Menu Close

Category: Others

f-C-C-a-b-R-2-a-lt-b-f-z-a-f-b-z-sin-zpi-b-a-f-z-z-2-z-a-b-2-f-z-0-z-

Question Number 2362 by 123456 last updated on 18/Nov/15 $${f}:\mathbb{C}\rightarrow\mathbb{C},\left({a},{b}\right)\in\mathbb{R}^{\mathrm{2}} ,{a}<{b} \\ $$$${f}\left({z}−{a}\right)={f}\left({b}−{z}\right)\mathrm{sin}\:\frac{{z}\pi}{{b}−{a}} \\ $$$${f}\left({z}\right)={z}^{\mathrm{2}} ,\Re\left({z}\right)\geqslant\frac{{a}+{b}}{\mathrm{2}} \\ $$$${f}\left({z}\right)=\mathrm{0},{z}=? \\ $$ Commented by Rasheed Soomro last…

Question-133394

Question Number 133394 by Dwaipayan Shikari last updated on 21/Feb/21 Commented by Dwaipayan Shikari last updated on 21/Feb/21 $${Three}\:{indentical}\:{point}\:{charges}\:,\:{each}\:{of}\:{mass}\:\boldsymbol{{m}}\:{and}\:{charge} \\ $$$$\boldsymbol{{Q}}\:,{hanging}\:{from}\:{three}\:{strings}\:.{Find}\:{the}\:{value}\:{of}\:\boldsymbol{{Q}}\:{in}\:{terms} \\ $$$${of}\:\boldsymbol{{m}},\boldsymbol{{L}}\:{and}\:\boldsymbol{\theta}\:\left({They}\:{are}\:{in}\:{equilibrium}\right) \\ $$…

1-1-1-2-1-2-1-1-3-2-1-3-2-2-2-1-5-2-1-3-5-2-3-3-pi-2-log-2-

Question Number 133381 by Dwaipayan Shikari last updated on 21/Feb/21 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }\left(\frac{\mathrm{1}}{\mathrm{2}.\mathrm{1}!}\right)+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }\left(\frac{\mathrm{1}.\mathrm{3}}{\mathrm{2}^{\mathrm{2}} .\mathrm{2}!}\right)+\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{2}} }\left(\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}}{\mathrm{2}^{\mathrm{3}} .\mathrm{3}!}\right)+…=\frac{\pi}{\mathrm{2}}{log}\left(\mathrm{2}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

suppose-that-f-0-1-R-lets-f-C-2-and-suppose-that-0-1-such-that-f-f-1-1-proof-or-give-a-counter-example-that-0-1-f-

Question Number 2289 by 123456 last updated on 14/Nov/15 $$\mathrm{suppose}\:\mathrm{that}\:{f}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R},\:\mathrm{lets}\:{f}\in\mathrm{C}^{\mathrm{2}} \\ $$$$\mathrm{and}\:\mathrm{suppose}\:\mathrm{that}\:\exists\alpha\in\left[\mathrm{0},\mathrm{1}\right]\:\mathrm{such}\:\mathrm{that} \\ $$$${f}\left(\alpha\right)+{f}\left(\mathrm{1}−\alpha\right)=\mathrm{1} \\ $$$$\mathrm{proof}\:\mathrm{or}\:\mathrm{give}\:\mathrm{a}\:\mathrm{counter}\:\mathrm{example}\:\mathrm{that} \\ $$$$\exists\xi\in\left[\mathrm{0},\mathrm{1}\right],{f}\left(\xi\right)=\xi \\ $$ Commented by Rasheed Soomro last…

n-1-cos-n-pi-n-4-1-48pi-4-1-12-1-1-pi-2-pi-4-90-

Question Number 133344 by Dwaipayan Shikari last updated on 21/Feb/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{cos}\left(\frac{{n}}{\pi}\right)}{{n}^{\mathrm{4}} }=−\frac{\mathrm{1}}{\mathrm{48}\pi^{\mathrm{4}} }+\frac{\mathrm{1}}{\mathrm{12}}\left(\mathrm{1}−\frac{\mathrm{1}}{\pi^{\mathrm{2}} }\right)+\frac{\pi^{\mathrm{4}} }{\mathrm{90}} \\ $$ Terms of Service Privacy Policy Contact:…

Find-modulus-and-argumen-of-z-1-i-4-3-i-7-1-i-2-8-1-i-3-12-

Question Number 133346 by bramlexs22 last updated on 21/Feb/21 $$\:\mathrm{Find}\:\mathrm{modulus}\:\mathrm{and}\:\mathrm{argumen}\:\mathrm{of}\: \\ $$$$\:\mathrm{z}\:=\:\frac{\left(\mathrm{1}−{i}\right)^{\mathrm{4}} \left(\sqrt{\mathrm{3}}+{i}\right)^{\mathrm{7}} }{\left(\mathrm{1}+{i}\sqrt{\mathrm{2}}\right)^{\mathrm{8}} \left(−\mathrm{1}−{i}\sqrt{\mathrm{3}}\right)^{\mathrm{12}} } \\ $$ Answered by mathmax by abdo last updated…