Question Number 143251 by aliibrahim1 last updated on 12/Jun/21 Answered by MJS_new last updated on 12/Jun/21 $$\mathrm{let}\:{x}={r}\mathrm{e}^{\mathrm{i}\theta} \wedge{r}>\mathrm{0}\wedge\mathrm{0}\leqslant\theta<\mathrm{2}\pi \\ $$$${r}\mathrm{e}^{\mathrm{i}\theta} +\frac{\mathrm{3}}{\:{r}^{\mathrm{1}/\mathrm{2}} \mathrm{e}^{\mathrm{i}\theta/\mathrm{2}} }=\mathrm{0} \\ $$$${r}^{\mathrm{3}/\mathrm{2}}…
Question Number 12173 by Mr Chheang Chantria last updated on 15/Apr/17 $$\boldsymbol{{Prove}}\:\boldsymbol{{that}}\:\forall\boldsymbol{{x}}\in\left[\mathrm{1},\mathrm{2}\right] \\ $$$$\Rightarrow\:\mathrm{1}−\boldsymbol{{x}}^{\mathrm{2}} \:\leqslant\:\boldsymbol{{x}} \\ $$ Answered by ajfour last updated on 18/Apr/17 $${x}\geqslant\mathrm{1}…
Question Number 12171 by uni last updated on 15/Apr/17 $$\int\mathrm{x}^{\mathrm{2}} ×\mathrm{sgn}\left(\mathrm{2x}\right)\mathrm{dx}=? \\ $$ Answered by mrW1 last updated on 15/Apr/17 $${f}\left({x}\right)={x}^{\mathrm{2}} ×{sgn}\left(\mathrm{2}{x}\right) \\ $$$$=\begin{cases}{{x}^{\mathrm{2}} \:\:\:{x}>\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:{x}=\mathrm{0}}\\{−{x}^{\mathrm{2}}…
Question Number 143240 by cesarL last updated on 11/Jun/21 $$\frac{\mathrm{2}}{{y}}=\frac{\mathrm{1}}{{x}}\left(\frac{{a}}{{y}}+\mathrm{1}\right) \\ $$$${x}=\mathrm{2}\left(\mathrm{4}{a}−{y}\right) \\ $$$${Is}\:{equations}\:{system} \\ $$ Answered by MJS_new last updated on 11/Jun/21 $$\frac{\mathrm{2}}{{y}}=\frac{\mathrm{1}}{{x}}\left(\frac{{a}}{{y}}+\mathrm{1}\right)\:\Leftrightarrow\:\mathrm{2}{x}={a}+{y}\:\Leftrightarrow\:{x}=\frac{{a}+{y}}{\mathrm{2}} \\…
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Question Number 143238 by BHOOPENDRA last updated on 11/Jun/21 Answered by mathmax by abdo last updated on 11/Jun/21 $$\Phi=\int_{\mathrm{C}} \frac{\mathrm{cos}\left(\pi\mathrm{z}^{\mathrm{2}} \right)+\mathrm{sin}\left(\pi\mathrm{z}^{\mathrm{2}} \right)}{\left(\mathrm{z}+\mathrm{1}\right)\left(\mathrm{z}+\mathrm{2}\right)}\mathrm{dz}\:\:\mathrm{let}\:\Psi\left(\mathrm{z}\right)=\frac{\mathrm{cos}\left(\pi\mathrm{z}^{\mathrm{2}} \right)+\mathrm{sin}\left(\pi\mathrm{z}^{\mathrm{2}} \right)}{\left(\mathrm{z}+\mathrm{1}\right)\left(\mathrm{z}+\mathrm{2}\right)} \\…
Question Number 12161 by tawa last updated on 15/Apr/17 Commented by mrW1 last updated on 16/Apr/17 $${only}\:{numerical}\:{solution}: \\ $$ Commented by mrW1 last updated on…
Question Number 143234 by mathdanisur last updated on 11/Jun/21 Answered by mr W last updated on 11/Jun/21 $${F}={x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} +\lambda\left(\alpha{x}+\alpha{y}+\gamma{z}−\mathrm{1}\right) \\ $$$$\frac{\partial{F}}{\partial{x}}=\mathrm{3}{x}^{\mathrm{2}} +\lambda\alpha=\mathrm{0}\: \\…
Question Number 143229 by loveineq last updated on 11/Jun/21 $$\mathrm{Let}\:{a},{b},{c}\:\geqslant\:\mathrm{0}\:\mathrm{and}\:\left(\mathrm{1}+{a}\right)\left(\mathrm{1}+{b}\right)\left(\mathrm{1}+{c}\right)\:=\:\mathrm{8}. \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({a}+\frac{\mathrm{2}{b}+\mathrm{1}}{{a}+{b}+\mathrm{1}}\right)\left({b}+\frac{\mathrm{2}{c}+\mathrm{1}}{{b}+{c}+\mathrm{1}}\right)\left({c}+\frac{\mathrm{2}{a}+\mathrm{1}}{{c}+{a}+\mathrm{1}}\right)\:\geqslant\:\mathrm{8}\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143231 by mnjuly1970 last updated on 11/Jun/21 $$…..{mathematical}\:……{Analysis}…. \\ $$$$\:{if}\:::\:\:\:\boldsymbol{\phi}\left({n}\right):=\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}^{\mathrm{2}{n}−\mathrm{1}} {log}\left(\mathrm{1}+{x}\right){dx} \\ $$$$\:{then}\:\:{find}\:\:{the}\:{value}\:{of}\:\:::\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\Theta:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \boldsymbol{\phi}\left({n}\right)\: \\ $$$$\:\:\:\:\:\:…….{m}.{n} \\…