Question Number 97270 by bobhans last updated on 07/Jun/20 $$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{all}}\:\boldsymbol{\mathrm{real}}\:\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{x}},\boldsymbol{\mathrm{y}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{z}}\:\boldsymbol{\mathrm{giving}} \\ $$$$\boldsymbol{\mathrm{answer}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{form}}\:\left(\boldsymbol{\mathrm{x}},\boldsymbol{\mathrm{y}},\boldsymbol{\mathrm{z}}\right)\:\begin{cases}{\boldsymbol{\mathrm{x}}\left(\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\right)+\boldsymbol{\mathrm{z}}\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{y}}\right)=\:\mathrm{4}}\\{\boldsymbol{\mathrm{y}}\left(\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{z}}\right)+\boldsymbol{\mathrm{x}}\left(\boldsymbol{\mathrm{y}}−\boldsymbol{\mathrm{z}}\right)\:=\:−\mathrm{4}}\\{\boldsymbol{\mathrm{z}}\left(\boldsymbol{\mathrm{z}}+\boldsymbol{\mathrm{x}}\right)+\boldsymbol{\mathrm{y}}\left(\boldsymbol{\mathrm{z}}−\boldsymbol{\mathrm{x}}\right)\:=\:\mathrm{5}}\end{cases} \\ $$ Commented by john santu last updated on 07/Jun/20 $$\left(\mathrm{1}\right)\:\mathrm{x}^{\mathrm{2}} +\mathrm{xy}+\mathrm{xz}−\mathrm{yz}\:=\:\mathrm{4} \\…
Question Number 31712 by gunawan last updated on 13/Mar/18 $$\mathrm{let}\:{f}\:\mathrm{convex}\:\mathrm{function}\:\mathrm{on}\:\left[\mathrm{0},\:\mathrm{2}\pi\right] \\ $$$$\mathrm{with}\:{f}\:''\left({x}\right)\:\leqslant\:{M}\:. \\ $$$$\mathrm{find}\:\mathrm{values}\:{a}\:\mathrm{and}\:{b}\:\:\mathrm{so} \\ $$$${a}\leqslant\int_{\mathrm{0}} ^{\mathrm{2}\pi} {f}\left({x}\right)\mathrm{cos}\:{x}\:{dx}\:\leqslant{bM} \\ $$ Terms of Service Privacy Policy…
Question Number 97231 by mathmax by abdo last updated on 07/Jun/20 $$\mathrm{developp}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie}\:\mathrm{f}\left(\mathrm{x}\right)\:=\frac{\mathrm{1}}{\mathrm{cos}^{\mathrm{2}} \mathrm{x}\:−\mathrm{3cosx}\:+\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 97230 by mathmax by abdo last updated on 07/Jun/20 $$\left.\mathrm{1}\right)\:\mathrm{developp}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{ln}\left(\mathrm{sinx}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{developp}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie}\:\mathrm{g}\left(\mathrm{x}\right)=\mathrm{ln}\left(\mathrm{cosx}\:+\mathrm{sinx}\right) \\ $$$$\left.\mathrm{3}\right)\mathrm{developp}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{seri}\:\mathrm{e}\:\mathrm{h}\left(\mathrm{x}\right)\:=\mathrm{ln}\left(\mathrm{cosx}\:+\mathrm{2sinx}\right) \\ $$ Answered by mathmax by abdo last updated…
Question Number 97226 by mathmax by abdo last updated on 07/Jun/20 $$\mathrm{let}\:\:\mathrm{a}_{\mathrm{n}} \:\mathrm{the}\:\mathrm{sequence}\:\mathrm{wich}\:\mathrm{verify}\:\mathrm{a}_{\mathrm{n}} \:+\mathrm{a}_{\mathrm{n}+\mathrm{1}} =\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{2}} } \\ $$$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\mathrm{a}_{\mathrm{n}} \mathrm{x}^{\mathrm{n}} \\ $$ Terms…
Question Number 31673 by gunawan last updated on 12/Mar/18 $$\mathrm{let}\:\mathrm{function}−\mathrm{function}\:{f}\:\mathrm{and}\:{g} \\ $$$$\mathrm{continues}\:\left[\:{a},\:{b}\right]\:\mathrm{and}\:\mathrm{diferensiabel} \\ $$$$\left({a},\:{b}\right).\:\mathrm{If}\:{f}'\left({x}\right)={g}'\left({x}\right)\neq\mathrm{0},\:\forall{x}\:\in\:\left({a},\:{b}\right) \\ $$$$\mathrm{and}\:{g}\left({a}\right)={a},\:{g}\left({b}\right)={b},\:\mathrm{find}\:\mathrm{value} \\ $$$$\mid{f}\left({b}\right)−{f}\left({a}\right)\mid. \\ $$ Terms of Service Privacy Policy…
Question Number 31546 by prof Abdo imad last updated on 10/Mar/18 $${let}\:{consider}\:{the}\:{numrtical}\:{function} \\ $$$${f}\left({x}\right)=\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} \:+{x}+\mathrm{1}}\:\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{then}\:{give} \\ $$$${f}^{\left({n}\right)} \left(\mathrm{0}\right). \\ $$ Answered by prof Abdo…
Question Number 31531 by abdo imad last updated on 09/Mar/18 $${let}\:{give}\:{f}\left({x}\right)=\frac{\mathrm{1}}{{x}}\:+\sum_{{n}=\mathrm{1}} ^{\infty} \:\left(\frac{\mathrm{1}}{{x}+{n}}\:+\frac{\mathrm{1}}{{x}−{n}}\right)\:{with}\:{x}\in{R}−{Z} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{the}\:{existence}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:{f}\:{is}\:\mathrm{1}−{periodic} \\ $$$$\left.\mathrm{3}\right){prove}\:{that}\:{f}\left(\frac{{x}}{\mathrm{2}}\right)\:+{f}\left(\frac{{x}+\mathrm{1}}{\mathrm{2}}\right)=\mathrm{2}{f}\left({x}\right). \\ $$ Terms of Service Privacy…
Question Number 31533 by abdo imad last updated on 09/Mar/18 $${let}\:{put}\:{S}\left({x}\right)=\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}+{x}} \\ $$$$\left.\mathrm{1}\left.\right)\:{prove}\:{that}\:{S}\:{is}\:{C}^{\mathrm{1}} \:{on}\right]\mathrm{0}'+\infty\left[\right. \\ $$$$\left.\mathrm{2}\right){give}\:{the}\:{variation}\:{of}\:{S}\left({x}\right) \\ $$$$\left.\mathrm{3}\right){prove}\:{that}\:\forall{x}>\mathrm{0}\:{S}\left({x}+\mathrm{1}\right)+{S}\left({x}\right)=\frac{\mathrm{1}}{{x}} \\ $$$$\left.\mathrm{4}\right){give}\:{a}\:{equivalent}\:{for}\:{S}\:{at}\:\mathrm{0} \\ $$$$\left.\mathrm{5}\right){find}\:{a}\:{equivalent}\:{for}\:{S}\:{at}\:+\infty.…
Question Number 31526 by abdo imad last updated on 09/Mar/18 $$\left.\mathrm{1}\right){find}\:{lim}_{{n}\rightarrow\infty} \left(\:\frac{{a}^{\frac{\mathrm{1}}{{n}}} \:+{b}^{\frac{\mathrm{1}}{{n}}} }{\mathrm{2}}\right)^{{n}} \\ $$$$\left.\mathrm{2}\right)\:{let}\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}}\:{calculate}\:{lim}_{{n}\rightarrow\infty} \:\frac{\mathrm{1}}{\mathrm{2}^{{n}} }\left(\:^{{n}} \sqrt{{cos}\theta}\:+^{{n}} \sqrt{{sin}\theta}\:\right)^{{n}} \\ $$ Commented by abdo…