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Question-136950

Question Number 136950 by BHOOPENDRA last updated on 28/Mar/21 Answered by Olaf last updated on 28/Mar/21 $$\overset{\wedge} {{f}}\:^{{c}} \left(\nu\right)\:=\:\int_{−\infty} ^{+\infty} {f}\left({s}\right)\mathrm{cos}\left(\mathrm{2}\pi\nu{s}\right){ds}\:=\:\mathrm{Re}\overset{\wedge} {{f}}\left(\nu\right) \\ $$$$\mathcal{F}\left(\frac{\mathrm{1}}{{s}}\right)\:=\:−{i}\pi\mathrm{sign}\left(\nu\right) \\…

what-is-the-intutive-understanding-of-eigenvalues-and-vectors-with-practical-examples-

Question Number 5859 by wanderer last updated on 02/Jun/16 $${what}\:{is}\:{the}\:{intutive}\:{understanding}\:{of}\: \\ $$$${eigenvalues}\:{and}\:{vectors}.{with}\:{practical}\: \\ $$$${examples}. \\ $$ Commented by FilupSmith last updated on 02/Jun/16 $$\mathrm{A}\:\mathrm{vector}\:\mathrm{is}\:\mathrm{a}\:\mathrm{direction}\:\mathrm{and}\:\mathrm{magnitude}. \\…

Question-136899

Question Number 136899 by BHOOPENDRA last updated on 27/Mar/21 Answered by Olaf last updated on 28/Mar/21 $$\mathrm{3}. \\ $$$${f}\left({x}\right)\:=\:{x}^{\mathrm{2}} ,\:−\mathrm{2}\leqslant{x}\leqslant\mathrm{2} \\ $$$${a}_{\mathrm{0}} \left({f}\right)\:=\:\frac{\mathrm{1}}{\mathrm{T}}\int_{−\frac{\mathrm{T}}{\mathrm{2}}} ^{+\frac{\mathrm{T}}{\mathrm{2}}} {f}\left({x}\right){dx}…

Question-136885

Question Number 136885 by BHOOPENDRA last updated on 27/Mar/21 Answered by bramlexs22 last updated on 27/Mar/21 $$\lambda^{\mathrm{3}} −\left(\mathrm{trace}\:\mathrm{A}\right)\lambda^{\mathrm{2}} +\:\begin{pmatrix}{\mathrm{minor}\:\mathrm{of}\:\mathrm{the}\:\mathrm{terms}}\\{\mathrm{on}\:\mathrm{the}\:\mathrm{leading}\:\mathrm{diag}\:\mathrm{A}\:}\end{pmatrix}\lambda−\mathrm{det}\left(\mathrm{A}\right)=\mathrm{0} \\ $$$$\lambda^{\mathrm{3}} −\mathrm{3}\lambda^{\mathrm{2}} +\left(\begin{vmatrix}{\mathrm{1}\:\:\mathrm{2}}\\{\mathrm{2}\:\:\mathrm{1}}\end{vmatrix}+\begin{vmatrix}{\mathrm{1}\:\:\:\mathrm{0}}\\{\mathrm{1}\:\:\:\mathrm{1}}\end{vmatrix}+\begin{vmatrix}{\:\:\mathrm{1}\:\:\:\:\:\mathrm{2}}\\{−\mathrm{1}\:\:\:\mathrm{1}}\end{vmatrix}\right)\lambda−\mathrm{3}\:=\mathrm{0} \\ $$$$\lambda^{\mathrm{3}}…

64-1-6-Is-there-any-short-cut-for-mcq-

Question Number 71326 by sadimuhmud 136 last updated on 13/Oct/19 $$\left(−\mathrm{64}\right)^{\frac{\mathrm{1}}{\mathrm{6}}} =?\left(\boldsymbol{\mathrm{I}}\mathrm{s}\:\mathrm{there}\:\mathrm{any}\:\mathrm{short}\:\mathrm{cut}\:\mathrm{for}\:\mathrm{mcq}\right) \\ $$ Answered by MJS last updated on 13/Oct/19 $$\mathrm{2}^{\mathrm{6}} =\mathrm{64}\:\Rightarrow\:\sqrt[{\mathrm{6}}]{−\mathrm{64}}=\mathrm{2i} \\ $$…

n-a-n-n-1-2-b-n-n-1-2-1-2a-2-pi-0-e-t-2-2-1-a-ab-cosh-log-ab-t-a-3-b-2a-ab-cosh-log-ab-t-dt-

Question Number 136850 by Dwaipayan Shikari last updated on 26/Mar/21 $$\underset{{n}=−\infty} {\overset{\infty} {\sum}}{a}^{\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}}} {b}^{\frac{{n}\left({n}−\mathrm{1}\right)}{\mathrm{2}}} =\mathrm{1}+\sqrt{\frac{\mathrm{2}{a}^{\mathrm{2}} }{\pi}}\int_{\mathrm{0}} ^{\infty} {e}^{−{t}^{\mathrm{2}} /\mathrm{2}} \left(\frac{\mathrm{1}−{a}\sqrt{{ab}}\:{cosh}\left(\sqrt{{log}\left({ab}\right)}\:{t}\right)}{{a}^{\mathrm{3}} {b}−\mathrm{2}{a}\sqrt{{ab}\:}\:{cosh}\left(\sqrt{{log}\left({ab}\right)}\:{t}\right)}\right){dt} \\ $$ Commented by…