Question Number 1842 by 123456 last updated on 12/Oct/15 $${f}\left({x},{y}\right)={f}\left({x}+{y},{xy}\right) \\ $$$${f}\left({x},{y}\right)={x},−\mathrm{2}\leqslant{y}\leqslant\mathrm{2} \\ $$$${f}\left({x},{y}\right)={y},\mid{x}\mid\geqslant\mathrm{100}\vee\mid{y}\mid\geqslant\mathrm{100} \\ $$$${f}\left(\mathrm{0},\mathrm{0}\right)=? \\ $$$${f}\left(\mathrm{1},\mathrm{4}\right)=? \\ $$ Commented by 123456 last updated…
Question Number 67379 by mathmax by abdo last updated on 26/Aug/19 $${let}\:\:{f}\left({x}\right)\:={e}^{−\mid{x}\mid} \:\:\:\:\:\:\mathrm{2}\pi\:\:{periodic}\:{even} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$ Commented by Abdo msup. last updated on 28/Aug/19…
Question Number 67236 by prof Abdo imad last updated on 24/Aug/19 $${let}\:{T}_{{n}} ={cos}\left({narccosx}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculste}\:{T}_{\mathrm{0}} ,{T}_{\mathrm{1}} ,{T}_{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right){find}\:\:{roots}\:{of}\:{T}_{{n}} \\ $$$$\left.\mathrm{3}\right){decompose}\:\:{the}\:{fraction}\:{F}\:=\frac{\mathrm{1}}{{T}_{{n}} } \\ $$ Commented…
Question Number 67234 by prof Abdo imad last updated on 24/Aug/19 $${factorise}\:{p}\left({x}\right)=\mathrm{1}+{x}+{x}^{\mathrm{2}} \:+{x}^{\mathrm{3}} \:+{x}^{\mathrm{5}} \\ $$$${inside}\:{C}\left[{x}\right]\:{and}\:{R}\left[{x}\right] \\ $$$${calculate}\:{p}\left({e}^{{i}\frac{\pi}{\mathrm{5}}} \right)\:{and}\:{p}\left({cos}\left(\frac{\pi}{\mathrm{5}}\right)\right) \\ $$ Commented by mathmax by…
Question Number 67232 by prof Abdo imad last updated on 24/Aug/19 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{cos}\left({n}\frac{\pi}{\mathrm{3}}\right)}{{n}} \\ $$ Commented by mathmax by abdo last updated on 25/Aug/19…
Question Number 1668 by 123456 last updated on 30/Aug/15 $$\frac{{f}\left({x}\right)+{f}\left({y}\right)}{\mathrm{2}}={f}\left(\frac{{x}+{y}}{\mathrm{2}}\right),\forall{x},{y}\in\mathbb{R} \\ $$$${f}\left({x}\right)=? \\ $$ Commented by Rasheed Ahmad last updated on 30/Aug/15 $${f}\left({x}\right)\:{has}\:{two}\:{properties}: \\ $$$$\left(\mathrm{1}\right)\:{f}\left({cx}\right)={cf}\left({x}\right)\:{for}\:{constant}\:{c}…
Question Number 67189 by mathmax by abdo last updated on 23/Aug/19 $${solve}\:{inside}\:{R}^{\mathrm{3}} \:{the}\:{system}\:\begin{cases}{\mathrm{2}{x}+{y}+{z}\:=\mathrm{1}}\\{{x}+\mathrm{2}{y}+{z}\:=\mathrm{2}}\end{cases} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left\{{x}+{y}+\mathrm{2}{z}\:=\mathrm{3}\right. \\ $$ Answered by MJS last updated on 23/Aug/19 $${D}=\begin{vmatrix}{\mathrm{2}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{2}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{2}}\end{vmatrix}=\mathrm{4}…
Question Number 67187 by mathmax by abdo last updated on 23/Aug/19 $${let}\:{f}\left({x}\right)\:={arctan}\left({x}^{\mathrm{3}} \right) \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}^{\left({n}\right)} \left({x}\right){and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\left({x}^{\mathrm{3}} \right){dx} \\…
Question Number 1635 by 123456 last updated on 28/Aug/15 $$\mathrm{lets}\:{x}>\mathrm{0},\:\mathrm{and}\:\mathrm{take}\:\mathrm{the}\:\mathrm{sequence}\:{a} \\ $$$${a}_{\mathrm{0}} =\sqrt{{x}} \\ $$$${a}_{{n}+\mathrm{1}} =\sqrt{{x}+{a}_{{n}} } \\ $$$$\mathrm{i}.\mathrm{proof}\:\mathrm{that}\:\mathrm{0}\leqslant{a}_{{n}} \leqslant{a}_{{n}+\mathrm{1}} \\ $$$$\mathrm{ii}.\mathrm{proof}\:\mathrm{that}\:\exists\mathrm{M}\:\mathrm{such}\:\mathrm{that}\:{a}_{{n}} \leqslant\mathrm{M} \\ $$$$\mathrm{iii}.\mathrm{using}\:\mathrm{i}\:\mathrm{and}\:\mathrm{ii}\:\mathrm{proof}\:\mathrm{that}\:\underset{{n}\rightarrow\infty}…
Question Number 67055 by Tony Lin last updated on 22/Aug/19 $${let}\:\mathbb{Z}_{+} =\mathbb{N}\cup\left\{\mathrm{0}\right\},\:{f}:\:\mathbb{Z}_{+} ×\mathbb{Z}_{+} \rightarrow\mathbb{Z}_{+} \\ $$$${f}\left({m},\:{n}\right)=\frac{\left({m}+{n}\right)\left({m}+{n}+\mathrm{1}\right)}{\mathrm{2}}+{m} \\ $$$${prove}\:{that}\:{f}\:{is}\:{a}\:{one}-{to}-{one}\:{function} \\ $$$${and}\:{also}\:{an}\:{onto}\:{function} \\ $$ Terms of Service…