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 581 by 123456 last updated on 31/Jan/15 $${z}^{\mathrm{2}} =\mathrm{cos}\:\theta+{i}\mathrm{sin}\:\theta \\ $$$${z}=? \\ $$ Answered by ssahoo last updated on 31/Jan/15 $${e}^{{i}\theta} =\mathrm{cos}\:\theta\:+{i}\mathrm{sin}\:\theta={z}^{\mathrm{2}} \\…
Question Number 131654 by mohammad17 last updated on 07/Feb/21 $$\underset{\mathrm{0}} {\int}^{\:\mathrm{1}/\mathrm{64}} \frac{{tan}^{−\mathrm{1}} {x}}{\:\sqrt{{x}}}{dx} \\ $$ Answered by mathmax by abdo last updated on 07/Feb/21 $$\mathrm{I}=\int_{\mathrm{0}}…
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 $${Let}\:{e}^{\mathrm{2}{x}} +\mathrm{cos}\:\mathrm{2}{x}={z} \\…
Question Number 66115 by Rio Michael last updated on 09/Aug/19 $$\:{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 577 by Bek last updated on 31/Jan/15 $${x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}=\mathrm{0} \\ $$$$ \\ $$ Answered by Bek last updated on 31/Jan/15 $$ \\ $$…
Question Number 131644 by Ahmed1hamouda last updated on 07/Feb/21 Commented by Ahmed1hamouda last updated on 07/Feb/21 $$ \\ $$$$\mathrm{solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation} \\ $$ Answered by rs4089 last…
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 66109 by Rio Michael last updated on 09/Aug/19 Commented by Rio Michael last updated on 09/Aug/19 $${The}\:{diagram}\:{above}\:{shows}\:{a}\:{uniform}\:{semi}−{circular}\:{lamina}\:{of}\:{radius}\:\mathrm{2}{a} \\ $$$$,{center}\:{O}.\:{The}\:{distance}\:{of}\:{the}\:{centre}\:{of}\:{mass}\:{form}\:{P},\:{vertically}\:{above}\:{O}\:{is} \\ $$$$ \\ $$$${A}\:\:\frac{\mathrm{6}{a}\pi−\mathrm{8}{a}}{\mathrm{3}\pi}…
Question Number 572 by kth last updated on 29/Jan/15 $${xy}=\mathrm{6}\left({x}+{y}\right) \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{325} \\ $$$${x}=? \\ $$$${y}=? \\ $$$$ \\ $$ Answered by prakash…