Question Number 159532 by HongKing last updated on 18/Nov/21 $$\mathrm{if}\:\:\mathrm{0}<\mathrm{a}\leqslant\mathrm{b}\:\:\mathrm{then}: \\ $$$$\underset{\:\boldsymbol{\mathrm{a}}} {\overset{\:\boldsymbol{\mathrm{b}}} {\int}}\:\frac{\mathrm{x}^{\mathrm{19}} }{\:\sqrt{\mathrm{1}\:+\:\mathrm{x}^{\mathrm{30}} }}\:\mathrm{dx}\:\geqslant\:\mathrm{log}\:\sqrt[{\mathrm{10}}]{\frac{\mathrm{2}\:+\:\mathrm{b}^{\mathrm{20}} }{\mathrm{2}\:+\:\mathrm{a}^{\mathrm{20}} }} \\ $$$$ \\ $$ Terms of Service…
Question Number 159529 by HongKing last updated on 18/Nov/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\begin{cases}{\mathrm{2x}^{\mathrm{2}} \:+\:\mathrm{3y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}} \:=\:\mathrm{7}}\\{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}} \:=\:\sqrt{\mathrm{2}}\:\mathrm{z}\:\left(\mathrm{x}\:+\:\mathrm{y}\right)}\end{cases} \\ $$$$ \\ $$ Answered by 1549442205PVT…
Question Number 159534 by HongKing last updated on 18/Nov/21 $$\mathrm{Find}: \\ $$$$\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\mathrm{arctan}^{\mathrm{2}} \:\left(\mathrm{x}\right)\:\mathrm{dx} \\ $$$$ \\ $$ Answered by chhaythean last updated on…
Question Number 159530 by HongKing last updated on 18/Nov/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 159528 by HongKing last updated on 18/Nov/21 $$\mathrm{Find}: \\ $$$$\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\frac{\boldsymbol{\pi}}{\mathrm{6}}} {\int}}\frac{\mathrm{sin}\left(\mathrm{x}\right)\centerdot\mathrm{sin}\left(\mathrm{x}\:+\:\frac{\pi}{\mathrm{3}}\right)\centerdot\mathrm{sin}\left(\mathrm{x}\:+\:\frac{\mathrm{2}\pi}{\mathrm{3}}\right)}{\mathrm{sin}\left(\mathrm{3x}\right)\:+\:\mathrm{cos}\left(\mathrm{3x}\right)}\:\mathrm{dx} \\ $$$$\mathrm{Answer}:\:\:\frac{\pi}{\mathrm{48}} \\ $$ Answered by mnjuly1970 last updated on 18/Nov/21…
Question Number 159527 by HongKing last updated on 18/Nov/21 Commented by mr W last updated on 18/Nov/21 $${only}\:{x}=\frac{\mathrm{23}}{\mathrm{24}} \\ $$ Commented by HongKing last updated…
Question Number 159517 by Khalmohmmad last updated on 18/Nov/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\left({e}^{−\mathrm{2}{x}} −\frac{\mathrm{1}+{ax}}{\mathrm{1}+{bx}}\right) \\ $$$${a}+{b}=? \\ $$ Commented by tounghoungko last updated on 18/Nov/21 $$\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 28435 by abdo imad last updated on 25/Jan/18 $${find}\:{Q}\left({x}\right)\:/\:{nx}^{{n}+\mathrm{1}} −\left({n}+\mathrm{1}\right){x}^{{n}} +\mathrm{1}\:=\left({x}−\mathrm{1}\right)^{\mathrm{2}} {Q}\left({x}\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28434 by abdo imad last updated on 25/Jan/18 $${let}\:{give}\:{the}\:{polynomial}\:{p}\left({x}\right)=\left({x}+\mathrm{1}\right)^{{n}} −\left({x}−\mathrm{1}\right)^{{n}} {with}\:{n} \\ $$$${from}\:{N}^{\ast} \\ $$$$\left.\mathrm{1}\right)\:{give}\:{the}\:{factorisation}\:{of}\:{p}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} {cotan}\left(\frac{{k}\pi}{\mathrm{2}{p}+\mathrm{1}}\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}{p}+\mathrm{1}}} \\ $$ Terms of…
Question Number 28432 by abdo imad last updated on 25/Jan/18 $${let}\:{put}\:{w}={e}^{{i}\frac{\mathrm{2}\pi}{{n}}} \:{calculate}\:\:{S}_{{n}} =\:\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:\:\frac{\mathrm{1}}{{x}−{w}^{{k}} }\:\:{and} \\ $$$${W}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:\frac{\mathrm{1}}{\left({x}−{w}^{{k}} \right)^{\mathrm{2}} }\:. \\ $$…