Question Number 588 by shaleen last updated on 03/Feb/15 $$\left({a}+{b}=\mathrm{10}\right)\:\left({a}+{c}=\mathrm{24}\right)\:\left({b}+{c}=\mathrm{20}\right) \\ $$$${find}\:{a}\:{b}\:{c} \\ $$ Answered by prakash jain last updated on 03/Feb/15 $${a}+{b}=\mathrm{10}\Rightarrow{b}=\mathrm{10}−{a} \\ $$$${a}+{c}=\mathrm{24}\Rightarrow{c}=\mathrm{24}−{a}…
Question Number 585 by 123456 last updated on 02/Feb/15 $${f}_{{n}} \left({x}\right)=\left(\mathrm{1}+\frac{{x}}{{n}}\right)^{{nx}} ,{n}\in\mathbb{N}^{\ast} ,{x}\in\mathbb{R},{x}\geqslant\mathrm{0} \\ $$$$\underset{{n}\rightarrow+\infty} {\mathrm{lim}}\:{f}_{{n}} \left({x}\right)= \\ $$ Answered by prakash jain last updated…
Question Number 582 by ssahoo last updated on 31/Jan/15 $$\mathrm{Show}\:\mathrm{that} \\ $$$$\sqrt{\mathrm{5}+\sqrt{\mathrm{21}}}\:+\sqrt{\mathrm{8}+\sqrt{\mathrm{55}}}\:=\sqrt{\mathrm{7}+\sqrt{\mathrm{33}}}\:+\sqrt{\mathrm{6}+\sqrt{\mathrm{35}}} \\ $$ Commented by prakash jain last updated on 31/Jan/15 $$\sqrt{\mathrm{5}+\sqrt{\mathrm{21}}}={a}+{b} \\ $$$${a}^{\mathrm{2}}…
Question Number 66116 by Rio Michael last updated on 09/Aug/19 $${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…