Question Number 61529 by maxmathsup by imad last updated on 04/Jun/19 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:{x}^{\mathrm{2}} {e}^{−{zx}^{\mathrm{2}} } {dx}\:\:{with}\:{z}\:{from}\:{C}\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 61528 by maxmathsup by imad last updated on 04/Jun/19 $${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:{cos}\left({zx}^{\mathrm{2}} \right){dx}\:{with}\:{z}\:\in\:{C}\:. \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 192597 by York12 last updated on 22/May/23 $${a}_{\mathrm{1}\:} \:,\:{a}_{\mathrm{2}} \:,\:{a}_{\mathrm{3}\:} \:,\:….\:,\:{a}_{{n}} \:{is}\:{a}\:{sequence}\:{satifies}\:{that} \\ $$$${a}_{{n}+\mathrm{2}} ={a}_{{n}+\mathrm{1}} −{a}_{{n}} \:{for}\:{n}\:\geq\:\mathrm{1}.\:{suppose}\:{the}\:{sum}\: \\ $$$${of}\:{the}\:{first}\:\mathrm{999}\:{terms}\:=\:\mathrm{1003}\:{and}\:{the}\:{sum} \\ $$$${of}\:{the}\:{first}\:\mathrm{1003}\:{terms}\:=\:−\mathrm{999}\:{find}\:{the}\: \\ $$$${sum}\:{of}\:{the}\:{first}\:\mathrm{2002}\:{terms}.…
Question Number 192596 by York12 last updated on 22/May/23 Answered by a.lgnaoui last updated on 24/May/23 $$\left(\mathrm{x}_{\mathrm{m}} +\mathrm{iy}_{\mathrm{m}} \right)^{\mathrm{2}\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}}\right)} =\mathrm{1}\Leftrightarrow\left[\left(\mathrm{x}_{\mathrm{m}} +\mathrm{iy}_{\mathrm{m}} \right)^{\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}}} −\mathrm{1}\right]×\left[\left(\mathrm{x}_{\mathrm{m}} +\mathrm{iy}_{\mathrm{m}} \right)^{\mathrm{n}+\frac{\mathrm{1}}{\mathrm{n}}}…
Question Number 61526 by Jarbas last updated on 04/Jun/19 $${Solve}\:{for}\:{n}:\:{D}/{A}×\left\{\mathrm{1}−\frac{{P}×\left(\frac{\left(\mathrm{1}+{i}\right)^{{n}} ×{i}}{\left(\mathrm{1}+{i}\right)^{{n}} −\mathrm{1}}\right)}{\left({P}×\left(\frac{\left(\mathrm{1}+{i}\right)^{{r}} ×{i}}{\left(\mathrm{1}+{i}\right)^{{r}} −\mathrm{1}}\right)\right)−\frac{{R}}{{i}}×\left[\left(\frac{\mathrm{1}}{{n}}+{i}\right)×\left(\frac{\left(\mathrm{1}+{i}\right)^{{r}} ×{i}}{\left(\mathrm{1}+{i}\right)^{{r}} −\mathrm{1}}\right)−\left(\frac{\mathrm{1}}{{n}}+{i}\right)×\left(\frac{\left(\mathrm{1}+{i}\right)^{{n}} ×{i}}{\left(\mathrm{1}+{i}\right)^{{n}} −\mathrm{1}}\right)\right]}\right\}−\mathrm{1}=\mathrm{0} \\ $$$$ \\ $$ Terms of Service…
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Question Number 61522 by YSN 1905 last updated on 03/Jun/19 $${I}=\int\frac{\mathrm{sin}\:{x}.{e}^{\mathrm{cos}\:{x}} −\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right){e}^{\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right)} }{{e}^{\mathrm{2sin}\:{x}} −\mathrm{2}{e}^{\mathrm{sin}\:{x}} +\mathrm{1}}{dx} \\ $$ Answered by perlman last updated on 04/Jun/19 $${I}=\int\frac{{sin}\left({x}\right){e}^{{cos}\left({x}\right)}…
Question Number 127056 by Khalmohmmad last updated on 26/Dec/20 Answered by Olaf last updated on 26/Dec/20 $$\frac{\mathrm{25}{e}}{\mathrm{0}^{−} }\:=\:−\infty \\ $$ Terms of Service Privacy Policy…
Question Number 61521 by necx1 last updated on 03/Jun/19 Answered by ajfour last updated on 04/Jun/19 Commented by ajfour last updated on 04/Jun/19 $${FB}\:{line}=\frac{{b}}{\mathrm{4}}+\lambda\left({a}−\frac{{b}}{\mathrm{4}}\right) \\…