Question Number 61842 by psyche last updated on 10/Jun/19 $$\boldsymbol{{consider}}\:\boldsymbol{{the}}\:\boldsymbol{{space}}\:\boldsymbol{{P}}{n}\:\boldsymbol{{with}}\:\boldsymbol{{H}}=\left\{{f}:{f}\subset{Pn}\:\boldsymbol{{and}}\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right)\partial{x}=\mathrm{0}\right\}\:.\:{S}\boldsymbol{{how}}\:\boldsymbol{{that}}\:\boldsymbol{{H}}\:\boldsymbol{{is}}\:\boldsymbol{{a}}\:\boldsymbol{{S}}{UBSPACE}\:{of}\:{Pn}. \\ $$ Commented by arcana last updated on 10/Jun/19 $$\mathrm{define}\:\mathrm{P}_{{n}} \\ $$ Terms…
Question Number 192914 by ajfour last updated on 30/May/23 $${x}^{\mathrm{2}} \left({x}^{\mathrm{2}} −\mathrm{1}\right)=\left(\mathrm{1}−\frac{{c}}{{x}}\right)^{\mathrm{3}} +\left(\frac{{c}}{{x}}\right)^{\mathrm{3}} \\ $$ Answered by a.lgnaoui last updated on 31/May/23 $$\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)=\frac{\left(\mathrm{x}−\mathrm{c}\right)^{\mathrm{3}}…
Question Number 127377 by I want to learn more last updated on 29/Dec/20 Commented by zdf last updated on 29/Dec/20 $$ \\ $$ Commented by…
Question Number 61840 by psyche last updated on 10/Jun/19 $$\boldsymbol{{consider}}\:\boldsymbol{{the}}\:\boldsymbol{{triple}}\:\boldsymbol{{of}}\:\boldsymbol{{real}}\:\boldsymbol{{numbers}}\:\left(\boldsymbol{{x}},{y},{z}\right) \\ $$$${defined}\:{by}\:{the}\:{addittion}\:\left(\boldsymbol{{x}},{y},{z}\right)+\left({x}',{y}',{z}'\right)=\left({x}+{x}',{y}+{y}',{z}+{z}'\right) \\ $$$$\boldsymbol{{and}}\:\boldsymbol{{scalar}}\:\boldsymbol{{multiplication}}\:\boldsymbol{{by}}\:\:\:\boldsymbol{\alpha}\left({x},{y},{z}\right)=\left(\mathrm{0},\mathrm{0},\mathrm{0}\right).\: \\ $$$$\boldsymbol{{S}}{how}\:{that}\:{all}\:{axioms}\:{for}\:{a}\:{vector}\:{space}\:{are}\:{satisfied}\:{except}\:{axiom}\:\mathrm{8}. \\ $$ Answered by arcana last updated on 10/Jun/19…
Question Number 192909 by uchihayahia last updated on 30/May/23 $$\: \\ $$$$\:{let}\:{P}\left({x}\right)\:{is}\:{polinomial}\:{with}\:{integer} \\ $$$$\:{coefficient}\:{s}.{t}\:{P}\left(\mathrm{6}\right){P}\left(\mathrm{38}\right){P}\left(\mathrm{57}\right)+\mathrm{19}\:{is} \\ $$$$\:{divided}\:{by}\:\mathrm{114}.\:{P}\left(-\mathrm{13}\right)=\mathrm{479}\:{and}\:{P}\geqslant\mathrm{0} \\ $$$$\:{what}\:{is}\:{minimum}\:{value}\:{of}\:{P}\left(\mathrm{0}\right)? \\ $$$$ \\ $$ Terms of Service…
Question Number 127373 by mnjuly1970 last updated on 29/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{elemeary}\:\:\:{calculus}.. \\ $$$$\:\:{if}\:\:\:\:\begin{cases}{{sin}\left(\mathrm{3}{x}\right)+{cos}\left(\mathrm{3}{x}\right)={m}}\\{{sin}\left({x}\right)+{cos}\left({x}\right)={n}}\end{cases} \\ $$$$\:\:\:{then}\:\:\:{find}\:{the}\:{relatiomship} \\ $$$$\:\:\:{between}\:\:'{m}'\:{and}\:'\:{n}'\:{independent}\:{of} \\ $$$$\:\:'\:{x}'\:…. \\ $$ Answered by bemath last updated…
Question Number 127370 by mnjuly1970 last updated on 29/Dec/20 $$\:\:\:\:\:\:\:\:\:…\:\:{advanced}\:\:{calculus}\:\:.. \\ $$$$\:\:{prove}:: \\ $$$$\:\:\:\frac{\mathrm{1023}}{\mathrm{134}}\int_{\mathrm{0}} ^{\:\infty} \frac{{x}^{\frac{\mathrm{2}}{\mathrm{5}}} +{x}^{\frac{−\mathrm{2}}{\mathrm{5}}} }{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+\mathrm{1024}{x}^{\mathrm{2}} \right)}{dx}=\frac{\pi}{\varphi} \\ $$$$\:\:\:\varphi:\:{golden}\:\:{ratio}… \\ $$$$ \\…
Question Number 61835 by alphaprime last updated on 09/Jun/19 $$\mathrm{If}\:\alpha\:=\:\mathrm{Cis}\left(\mathrm{2}\pi/\mathrm{7}\right)\:\mathrm{and}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{A}_{\mathrm{0}} \:+\:\sum_{\mathrm{n}=\mathrm{1}} ^{\mathrm{14}} \mathrm{A}_{\mathrm{n}} \mathrm{x}^{\mathrm{n}} \: \\ $$$$\mathrm{Then}\:\mathrm{prove}\:\mathrm{that}\:\sum_{\alpha=\mathrm{0}} ^{\mathrm{6}} \mathrm{f}\left(\alpha^{\mathrm{n}} \mathrm{x}\right)=\:\mathrm{7}\left(\mathrm{A}_{\mathrm{0}} +\mathrm{A}_{\mathrm{7}} \mathrm{x}^{\mathrm{7}} +\mathrm{A}_{\mathrm{14}} \mathrm{x}^{\mathrm{14}} \right)…
Question Number 61834 by aliesam last updated on 09/Jun/19 Commented by maxmathsup by imad last updated on 09/Jun/19 $${let}\:{A}_{{n}} =\:\left\{\frac{\mathrm{1}}{{p}}\:\sum_{{k}=\mathrm{1}} ^{{p}} \:\left(\mathrm{1}+\frac{{k}}{{p}}\right)^{\frac{\mathrm{1}}{{n}}} \right\}^{{n}} \:\Rightarrow{ln}\left({A}_{{n}} \right)\:={n}\:{ln}\left(\frac{\mathrm{1}}{{p}}\sum_{{k}=\mathrm{1}}…
Question Number 127368 by I want to learn more last updated on 29/Dec/20 $$\int\:\frac{\sqrt{\mathrm{tan}\:\mathrm{x}}}{\:\sqrt{\mathrm{tan}^{\mathrm{2}} \mathrm{x}\:\:−\:\:\mathrm{1}}}\:\:\mathrm{dx} \\ $$ Answered by liberty last updated on 29/Dec/20 $$\:{let}\:\rightarrow\begin{cases}{\mathrm{tan}\:{x}\:\geqslant\mathrm{0}}\\{\mathrm{tan}^{\mathrm{2}}…