Question Number 66140 by AnjanDey last updated on 09/Aug/19 $$\mathrm{1}.\boldsymbol{{Show}}\:\boldsymbol{{that}}:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {f}\left(\mathrm{sin}\:\mathrm{2}{x}\right)\mathrm{sin}\:{x}\:{dx}=\sqrt{\mathrm{2}}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {f}\left(\mathrm{cos}\:\mathrm{2}{x}\right)\mathrm{cos}\:{x}\:{dx}. \\ $$$$\mathrm{2}.\boldsymbol{{If}}\:\boldsymbol{{f}}\left(\boldsymbol{{z}}\right)=\frac{\boldsymbol{{d}}}{\boldsymbol{{dz}}}\left\{\mathrm{5}^{\mid\boldsymbol{{f}}\left(\boldsymbol{{z}}\right)\mid} \right\}\:\:\boldsymbol{{then}}\:\boldsymbol{{what}}\:\boldsymbol{{is}}\:\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\boldsymbol{{f}}'\left(\boldsymbol{{e}}\right)? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 612 by 123456 last updated on 08/Mar/15 $${encontre}\:{f}:\mathbb{N}\rightarrow\mathbb{N}\:{sobrejetivo}\:{tal}\:{que} \\ $$$${f}^{−\mathrm{1}} \left({n}\right)=\left\{{m}\mid{f}\left({m}\right)={n}\right\}\:{e}\:{infinito} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 66116 by Rio Michael last updated on 09/Aug/19 $${Given}\:{that}\:\:{f}\left({x}\right)\:=\:\begin{cases}{{x},\:\:{for}\:\mathrm{0}\leqslant{x}<\mathrm{2}}\\{\mathrm{0},\:{for}\:\mathrm{2}\leqslant{x}\leqslant\mathrm{3}}\end{cases} \\ $$$${is}\:{periodic}\:{with}\:{period}\:\mathrm{3}\:{units}, \\ $$$${find}\:{the}\:{value}\:{of}\:\:{f}\left(\mathrm{5}\right)\:{and}\:{f}\left(−\mathrm{5}\right) \\ $$$${sketch}\:{the}\:{graph}\:{of}\:{f}\left({x}\right)\:{for}\:{x}\:{between}\:−\mathrm{3}\:{and}\:\mathrm{6} \\ $$$$ \\ $$$${please}\:{i}\:{really}\:{need}\:{explanations}\:{when}\:{solving}\:{the}\:{first}\:{part}\:{of}\:{the}\:{question} \\ $$$${thanks} \\ $$…
Question Number 66115 by Rio Michael last updated on 09/Aug/19 $$\:{find}\:\mid{z}\mid\:\:{where}\:{z}\:=\:\frac{\left(\mathrm{1}+{i}\sqrt{\mathrm{3}}\:\right)^{\mathrm{3}} }{\left(\mathrm{1}−{i}\right)^{\mathrm{3}} } \\ $$$${find}\:{the}\:{maximum}\:{value}\:{of}\:\:\:\mathrm{12}{sinx}\:−\:\mathrm{5}{cosx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 66114 by Rio Michael last updated on 09/Aug/19 $$\int\left(\frac{{e}^{\mathrm{2}{x}} −{sin}\mathrm{2}{x}}{{e}^{\mathrm{2}{x}} +{cos}\mathrm{2}{x}}\right){dx}\:=\:? \\ $$ Answered by $@ty@m123 last updated on 09/Aug/19 $${Let}\:{e}^{\mathrm{2}{x}} +\mathrm{cos}\:\mathrm{2}{x}={z} \\…
Question Number 66108 by Rio Michael last updated on 09/Aug/19 $${Given}\:{that}\:{the}\:{binomial}\:{expansion}\:{of}\:\frac{\mathrm{2}\:+\:{kx}}{\left(\mathrm{2}−\mathrm{5}{x}\right)^{\mathrm{2}\:} }\:,\:\mid{x}\mid\:<\:\frac{\mathrm{2}}{\mathrm{5}\:}\:,{in}\:{ascending} \\ $$$${powers}\:{of}\:{x}\:{is}\:\:\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\mathrm{7}}{\mathrm{4}}{x}\:+\:{Ax}^{\mathrm{2}} \:+\:…,\:{find}\:{the}\:{values}\:{of}\:{A}\:{and}\:{k} \\ $$ Commented by mr W last updated on 09/Aug/19…
Question Number 66107 by Rio Michael last updated on 09/Aug/19 $${Given}\:{that}\:{S}_{{n}} \:=\:\frac{{a}\left(\mathrm{1}\:−{r}^{{n}} \right)}{\mathrm{1}−{r}}\:,\:{r}\:\neq\:\mathrm{1},\:{show}\:{that}\:\frac{{S}_{\mathrm{3}{n}} \:−{S}_{\mathrm{2}{n}} }{{S}_{{n}} \:}\:=\:{r}^{\mathrm{2}{n}} \\ $$$${hence}\:{given}\:{that}\:{r}\:=\frac{\mathrm{1}}{\mathrm{2}}\:{find}\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{{S}_{\mathrm{3}{n}} \:−{S}_{\mathrm{2}{n}} }{{S}_{{n}} }\right) \\ $$…
Question Number 66104 by Rio Michael last updated on 09/Aug/19 $${f}\left({x}\right)=\:\mathrm{2}{x}^{\mathrm{3}} −{x}−\mathrm{4} \\ $$$${show}\:{that}\:{the}\:{equation}\:{f}\left({x}\right)\:=\mathrm{0}\:{has}\:{root}\:{between}\:\mathrm{1}\:{and}\:\mathrm{2} \\ $$$${show}\:{that}\:{the}\:{equation}\:{f}\left({x}\right)\:=\mathrm{0}\:{can}\:{be}\:{written}\:{as}\: \\ $$$$\:\:{x}\:=\:\sqrt{\left(\frac{\mathrm{2}}{{x}}\:+\frac{\mathrm{1}}{\mathrm{2}}\right)} \\ $$$${use}\:{the}\:{iteration} \\ $$$$\:{x}_{{n}+\mathrm{1}\:} \:=\:\sqrt{\left(\frac{\mathrm{2}}{{x}_{{n}} }\:+\frac{\mathrm{1}}{\mathrm{2}}\right)\:,} \\…
Question Number 66105 by Rio Michael last updated on 09/Aug/19 $${Find}\:\:\int_{−\mathrm{1}} ^{\mathrm{1}} \frac{\mathrm{9}\:+\mathrm{4}{x}^{\mathrm{2}} }{\mathrm{9}−\mathrm{4}{x}^{\mathrm{2}} }\:{dx} \\ $$ Commented by Prithwish sen last updated on 09/Aug/19…
Question Number 66103 by Rio Michael last updated on 09/Aug/19 $${A}\:{binary}\:{relation}\:{R}\:{is}\:{defined}\:{on}\:\mathbb{N},{the}\:{set}\:{of}\:{natural}\:{numbers}\:{by}\: \\ $$$$\:_{{x}} {R}_{{y}} \:\Leftrightarrow\:\exists\:{n}\:\in\:\mathbb{Z}\::\:{x}\:=\:\mathrm{2}^{{n}} {y},\:\:{x},{y}\:\in\:\mathbb{N} \\ $$$${show}\:{that}\:{R}\:{is}\:{an}\:{equivalence}\:{relation} \\ $$ Commented by Prithwish sen last…