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Question-67122

Question Number 67122 by sandeepkeshari0797@gmail.com last updated on 23/Aug/19 Answered by Cmr 237 last updated on 23/Aug/19 $$\mathrm{y}_{\mathrm{n}+\mathrm{2}} −\mathrm{2y}_{\mathrm{n}+\mathrm{1}} +\mathrm{y}_{\mathrm{n}} −\mathrm{n}^{\mathrm{2}} \mathrm{2}^{\mathrm{n}} =\mathrm{0} \\ $$$$\mathrm{l}'\mathrm{equation}\:\mathrm{caracteristique}\:\mathrm{est}:…

Let-is-cube-root-of-unity-and-x-y-z-Z-If-x-y-z-0-prove-that-3-x-y-z-Show-by-an-example-that-the-converse-is-not-true-

Question Number 1585 by Rasheed Soomro last updated on 22/Aug/15 $$\mathrm{Let}\:\omega\:\mathrm{is}\:\mathrm{cube}\:\mathrm{root}\:\mathrm{of}\:\mathrm{unity}\:\mathrm{and}\:\mathrm{x},\mathrm{y},\mathrm{z}\:\in\:\mathbb{Z} \\ $$$$\mathrm{If}\:\omega^{\mathrm{x}} +\omega^{\mathrm{y}} +\omega^{\mathrm{z}} =\mathrm{0}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{3}\:\mid\:\left(\mathrm{x}+\mathrm{y}+\mathrm{z}\right) \\ $$$$\mathrm{Show}\:{by}\:{an}\:{example}\:\mathrm{that}\:\mathrm{the}\:\mathrm{converse}\:\mathrm{is}\:{not}\:\:\mathrm{true}. \\ $$ Commented by 112358 last updated…

Let-and-denote-functions-of-x-where-is-odd-and-is-even-x-R-Is-it-generally-true-that-integrating-an-odd-function-gives-an-even-function-and-vice-versa-1-x-dx-1-x-C-and-2-x-d

Question Number 1582 by 112358 last updated on 21/Aug/15 $${Let}\:\phi\:{and}\:\varepsilon\:{denote}\:{functions}\:{of}\:{x} \\ $$$${where}\:\phi\:{is}\:{odd}\:{and}\:\varepsilon\:{is}\:{even}\:\forall{x}\in\mathbb{R}. \\ $$$${Is}\:{it}\:{generally}\:{true}\:{that}\:{integrating} \\ $$$${an}\:{odd}\:{function}\:{gives}\:{an}\:{even} \\ $$$${function}\:{and}\:{vice}\:{versa}?\: \\ $$$$\int\phi_{\mathrm{1}} \left({x}\right)\:{dx}=\varepsilon_{\mathrm{1}} \left({x}\right)+{C}\:? \\ $$$${and}\:\int\phi_{\mathrm{2}} \left({x}\right){dx}=\varepsilon_{\mathrm{2}}…

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Question Number 132655 by mohammad17 last updated on 15/Feb/21 $${write}\:\frac{\left(\mathrm{1}−{i}\right)^{\mathrm{23}} }{\left(\sqrt{\mathrm{3}}−{i}\right)^{\mathrm{13}} }\:{by}\:{re}^{{i}\theta} \:{such}\:{that}\:{r}>\mathrm{0},−\pi\leqslant\theta<\pi \\ $$ Answered by physicstutes last updated on 15/Feb/21 $$\mathrm{1}\:−{i}\:=\:\sqrt{\mathrm{2}}\:{e}^{−\frac{\pi}{\mathrm{4}}{i}} \\ $$$$\Rightarrow\:\left(\mathrm{1}−{i}\right)^{\mathrm{23}}…

Find-a-function-f-x-satisfying-the-following-equation-a-b-1-2-f-x-2-f-x-2-d-dx-f-x-2-dx-0-b-gt-0-a-gt-0-b-a-

Question Number 1581 by 112358 last updated on 21/Aug/15 $${Find}\:{a}\:{function}\:{f}\left({x}\right)\:{satisfying} \\ $$$${the}\:{following}\:{equation}. \\ $$$$\int_{{a}} ^{\:{b}} \left[\frac{\mathrm{1}}{\mathrm{2}}\left\{{f}\left({x}\right)\right\}^{\mathrm{2}} −\sqrt{\left\{{f}\left({x}\right)\right\}^{\mathrm{2}} +\left\{\frac{{d}}{{dx}}\left({f}\left({x}\right)\right)\right\}^{\mathrm{2}} }\right]{dx}=\mathrm{0} \\ $$$${b}>\mathrm{0},{a}>\mathrm{0}\:,\:{b}\neq{a}.\:\: \\ $$ Commented by…