Question Number 137316 by BHOOPENDRA last updated on 01/Apr/21 $${An}\:{alternating}\:{current}\:{after}\:{passing}\: \\ $$$$\:{through}\:{rectifire}\:{has}\:{the} \\ $$$${form}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{i}={I}_{\mathrm{0}} {sinx}\:\:\:\:\:\:{for}\:\mathrm{0}\leqslant{x}\leqslant\pi \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\:{for}\:\pi\leqslant{x}\leqslant\mathrm{2}\pi \\ $$$${where}\:{I}_{\mathrm{0}} \:{is}\:{the}\:{maximum}\:{current}\: \\ $$$${and}\:{period}\:{is}\:\mathrm{2}\pi.{express}\:{i}\:{is}\:{a}\: \\…
Question Number 6246 by FilupSmith last updated on 20/Jun/16 $$\mathrm{Need}\:\mathrm{help}\:\mathrm{solving}\:\int_{\mathrm{0}} ^{\:\infty} {x}^{−{x}} {dx} \\ $$$$\mathrm{My}\:\mathrm{current}\:\mathrm{working}: \\ $$$${x}^{−{x}} ={e}^{−{x}\mathrm{ln}{x}} \\ $$$${e}^{−{x}\mathrm{ln}{x}} =\mathrm{1}−{x}\mathrm{ln}\left({x}\right)+\frac{{x}^{\mathrm{2}} \mathrm{ln}\left({x}\right)^{\mathrm{2}} }{\mathrm{2}!}−\frac{{x}^{\mathrm{3}} \mathrm{ln}\left({x}\right)^{\mathrm{3}} }{\mathrm{3}!}+……
Question Number 137315 by liberty last updated on 01/Apr/21 $$\int_{\mathrm{0}} ^{\:\pi/\mathrm{4}} \:\sqrt{\mathrm{cos}\:^{\mathrm{3}} \left(\mathrm{2x}\right)}\:\mathrm{dx}\:? \\ $$ Answered by rs4089 last updated on 01/Apr/21 $$\int_{\mathrm{0}} ^{\:\pi/\mathrm{4}} \sqrt{{cos}^{\mathrm{3}}…
Question Number 71776 by TawaTawa last updated on 19/Oct/19 Answered by tw000001 last updated on 22/Oct/19 $$\mathrm{Use}\:\mathrm{Harmonic}\:\mathrm{series}\:\mathrm{to}\:\mathrm{solve}. \\ $$$${A}=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{4}}+…+\frac{\mathrm{1}}{\mathrm{2015}}−\frac{\mathrm{1}}{\mathrm{2016}} \\ $$$$=\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+…+\frac{\mathrm{1}}{\mathrm{2016}}\right)−\mathrm{2}\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{6}}+…+\frac{\mathrm{1}}{\mathrm{2016}}\right) \\ $$$$=\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+…+\frac{\mathrm{1}}{\mathrm{2016}}\right)−\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+…+\frac{\mathrm{1}}{\mathrm{1008}}\right) \\ $$$$={H}_{\mathrm{2016}}…
Question Number 137314 by liberty last updated on 01/Apr/21 $$ \\ $$The diagonals of a convex quadrilateral divide the area into A, B, D and…
Question Number 71777 by Henri Boucatchou last updated on 19/Oct/19 $$\:\:\underset{\boldsymbol{{n}}\rightarrow\infty} {\boldsymbol{{lim}}}\:\left(\frac{\boldsymbol{{n}}!\:+\:\mathrm{3}^{\boldsymbol{{n}}} }{\boldsymbol{{n}}^{\boldsymbol{{n}}} \:+\:\mathrm{3}^{\boldsymbol{{n}}} }\right)\:=\:? \\ $$ Commented by mathmax by abdo last updated on…
Question Number 6240 by sanusihammed last updated on 19/Jun/16 $$\int{e}^{{x}^{\mathrm{2}} } \:\:{dx}\: \\ $$ Commented by FilupSmith last updated on 20/Jun/16 $${I}=\int{e}^{{x}^{\mathrm{2}} } {dx} \\…
Question Number 6238 by sanusihammed last updated on 19/Jun/16 Answered by Yozzii last updated on 20/Jun/16 $${Let}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+{n}^{−\mathrm{1}} \right)^{−{n}^{\mathrm{2}} } ={l}. \\ $$$${Let}\:{u}={n}^{−\mathrm{1}} \Rightarrow{l}=\underset{{u}\rightarrow\mathrm{0}^{+} }…
Question Number 137311 by bramlexs22 last updated on 01/Apr/21 Answered by liberty last updated on 01/Apr/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
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