Question Number 196412 by Erico last updated on 25/Aug/23 $$\mathrm{Prove}\:\mathrm{that}\:\underset{\:{i}} {\int}^{\:+\infty} \left(\mathrm{cos2t}+\mathrm{isin2t}\right)\mathrm{e}^{−\mathrm{t}^{\mathrm{2}} } \mathrm{dt}=\:\frac{\sqrt{\pi}}{\mathrm{2e}} \\ $$ Commented by JDamian last updated on 24/Aug/23 $${is}\:\boldsymbol{\mathrm{t}}\:{real}\:{or}\:{complex}? \\…
Question Number 193204 by Mingma last updated on 07/Jun/23 Answered by witcher3 last updated on 08/Jun/23 $$\mathrm{H}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{k}}=\overset{\mathrm{1}} {\int}_{\mathrm{0}} \underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{x}^{\mathrm{k}−\mathrm{1}} \mathrm{dx}…
Question Number 65261 by shalinu last updated on 27/Jul/19 $${solve}\mathrm{4}−{xy}+{yz}−{xz} \\ $$ Commented by mr W last updated on 27/Jul/19 $${sir},\:{please}\:{explain}\:{your}\:{question}\:{a}\:{little}! \\ $$$${at}\:{the}\:{moment}\:{it}'{s}\:{not}\:{clear}\:{what} \\ $$$${your}\:{question}\:{is}.…
Question Number 64456 by ner0i last updated on 18/Jul/19 Commented by Tony Lin last updated on 18/Jul/19 $$\overset{\rightharpoonup} {{r}}'\left({t}\right)=\hat {{i}}−\frac{\mathrm{2}}{{t}^{\mathrm{2}} }\hat {{j}}−\frac{\mathrm{1}}{{t}^{\mathrm{2}} }\hat {{k}} \\…
Question Number 64011 by Prithwish sen last updated on 12/Jul/19 $$\mathrm{li}\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{m}}\frac{\mathrm{x}^{\mathrm{x}} −\mathrm{1}}{\mathrm{xlnx}} \\ $$ Commented by kaivan.ahmadi last updated on 12/Jul/19 $${y}={x}^{{x}} \Rightarrow{lny}={xlnx}\Rightarrow\frac{{y}'}{{y}}={lnx}+{x}×\frac{\mathrm{1}}{{x}}=\mathrm{1}+{lnx}\Rightarrow \\…
Question Number 128837 by BHOOPENDRA last updated on 10/Jan/21 Commented by BHOOPENDRA last updated on 10/Jan/21 $${without}\:{using}\:{gauss}\:{divergence}\:{theorm}\: \\ $$$${calculate}\:{surface}\:{integral}? \\ $$$${help}\:{me}\:{out}\:{this}? \\ $$ Terms of…
Question Number 128823 by BHOOPENDRA last updated on 10/Jan/21 Commented by BHOOPENDRA last updated on 10/Jan/21 $${help}\:{me}\:{out}\:{this}\:? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 128691 by BHOOPENDRA last updated on 09/Jan/21 $${find}\int\int_{{S}} \bigtriangledown×{F}\:.\hat {{n}ds} \\ $$$${where}\:{F}^{\rightarrow} ={y}^{\mathrm{2}} \hat {{i}}+{y}\hat {{j}}−{xz}\hat {{k}} \\ $$$${and}\:{S}\:{is}\:{the}\:{upper}\:{half}\:{of}\:{the}\:{sphere} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}}…
Question Number 128688 by BHOOPENDRA last updated on 09/Jan/21 $${find}\:{the}\:{flux}\:{of}\:{the}\:{vector}\:{field} \\ $$$${F}={x}\hat {{i}}+{y}\hat {{j}}+\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{1}\:\hat {{k}}} \\ $$$${through}\:{outer}\:{side}\:{of}\:{hyper}−{boloide} \\ $$$${z}=\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{1}} \\ $$$${bounded}\:{by}\:{the}\:{planes}\:…
Question Number 128592 by BHOOPENDRA last updated on 09/Jan/21 $$\int\int\int_{{V}} \bigtriangledown×{F}\:{dV}\:{where}\:{F}=\left({x}+\mathrm{2}{y}\right)\hat {{i}}−\mathrm{3}{z}\hat {{j}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+{x}\hat {{k}} \\ $$$${and}\:{V}\:{is}\:{the}\:{closed}\:{region}\:{in}\:{first}\:{octant} \\ $$$${by}\:{the}\:{plane}\:\mathrm{2}{x}+\mathrm{2}{y}+\mathrm{2}{z}=\mathrm{4} \\ $$$$ \\ $$ Answered…