Question Number 63517 by Rio Michael last updated on 05/Jul/19 $$\mathrm{Given}\:\mathrm{that}\:\:\mid{z}−\mathrm{6}\mid=\mathrm{2}\mid{z}+\mathrm{6}−\mathrm{9}{i}\mid, \\ $$$$\left.\mathrm{a}\right)\:\mathrm{Use}\:\mathrm{algebra}\:\mathrm{to}\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:{z}\:\mathrm{is}\:\mathrm{a}\:\mathrm{circle}, \\ $$$$\mathrm{stating}\:\mathrm{its}\:\mathrm{center}\:\mathrm{and}\:\mathrm{its}\:\mathrm{radius}. \\ $$$$\left.\mathrm{b}\right)\:\mathrm{sketch}\:\mathrm{the}\:\mathrm{locus}\:{z}\:\mathrm{on}\:\mathrm{an}\:\mathrm{argand}\:\mathrm{diagram}. \\ $$ Answered by MJS last updated on…
Question Number 129051 by oustmuchiya@gmail.com last updated on 12/Jan/21 $${prove}\:{that}\:\frac{\mathrm{1}+\boldsymbol{{sinx}}}{\boldsymbol{{sinxcosx}}}= \\ $$$$\boldsymbol{{tanx}}+\boldsymbol{{cotx}}+\boldsymbol{{secx}}\:\boldsymbol{{hence}} \\ $$$$\boldsymbol{{differentiate}}\:\boldsymbol{{the}}\:\boldsymbol{{function}} \\ $$ Answered by mindispower last updated on 12/Jan/21 $$\mathrm{1}={cos}^{\mathrm{2}} \left({x}\right)+{sin}^{\mathrm{2}}…
Question Number 129048 by bramlexs22 last updated on 12/Jan/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{Laplace}\:\mathrm{transform} \\ $$$$\mathrm{of}\:\mathrm{f}\left(\mathrm{t}\right)\:=\:−\mathrm{4t}^{\mathrm{2}} −\mathrm{5sin}\:\mathrm{3t}\: \\ $$ Answered by Dwaipayan Shikari last updated on 12/Jan/21 $$\mathscr{L}\left({f}\left({t}\right)\right)=−\mathrm{4}\int_{\mathrm{0}} ^{\infty}…
Question Number 129047 by Dwaipayan Shikari last updated on 12/Jan/21 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2}.\mathrm{1}!}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }\left(\frac{\mathrm{1}.\mathrm{3}}{\mathrm{2}^{\mathrm{2}} .\mathrm{2}!}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }\left(\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}}{\mathrm{2}^{\mathrm{3}} .\mathrm{3}!}\right)^{\mathrm{2}} +…=\frac{\sqrt{\pi}}{\Gamma^{\mathrm{2}} \left(\frac{\mathrm{3}}{\mathrm{4}}\right)} \\ $$ Answered by mindispower last…
Question Number 63510 by turbo msup by abdo last updated on 05/Jul/19 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{{t}^{{a}−\mathrm{1}} }{{x}+{t}}\:{dt}\:{with}\:{x}>\mathrm{0} \\ $$$${and}\:\mathrm{0}<{a}<\mathrm{1} \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{{t}^{{a}−\mathrm{1}} }{\left({x}+{t}\right)^{\mathrm{2}}…
Question Number 63509 by mathmax by abdo last updated on 05/Jul/19 $${calculate}\:\int_{−\mathrm{1}} ^{\mathrm{1}} \left(\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right){dx} \\ $$ Commented by Prithwish sen last updated on…
Question Number 63508 by mathmax by abdo last updated on 05/Jul/19 $${let}\:\:{f}\left({x}\right)\:=\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{dt}}{\left({t}^{\mathrm{2}} \:+{ixt}\:−\mathrm{1}\right)}\:\:{with}\:\mid{x}\mid>\mathrm{2}\:\:\:\left({i}^{\mathrm{2}} =−\mathrm{1}\right) \\ $$$$\left.\mathrm{1}\right)\:{extract}\:{Re}\left({f}\left({x}\right)\right)\:{and}\:{Im}\left({f}\left({x}\right)\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:\:{find}\:{olso}\:{g}\left({x}\right)\:=\int_{−\infty} ^{+\infty} \:\:\frac{{t}}{\left({t}^{\mathrm{2}} \:+{ixt}\:−\mathrm{1}\right)^{\mathrm{2}}…
Question Number 63507 by mathmax by abdo last updated on 05/Jul/19 $${let}\:{U}_{{n}} =\int_{\frac{\mathrm{1}}{{n}}} ^{\mathrm{1}} \left(\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}\:−\sqrt{{x}^{\mathrm{2}} −{x}+\mathrm{1}}\right){dx}\:\:\:\left({n}>\mathrm{0}\right) \\ $$$$\left.\mathrm{1}\right){calculate}\:{lim}_{{n}\rightarrow+\infty} \:\:{U}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:\:{find}\:{nature}\:{of}\:\:\Sigma\:{U}_{{n}} \\ $$ Answered…
Question Number 129041 by oustmuchiya@gmail.com last updated on 12/Jan/21 $${Differentiate}\:\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\left(\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{4}\right)^{\mathrm{3}} \left(\mathrm{6}\boldsymbol{{x}}^{\mathrm{2}} \right) \\ $$ Answered by bramlexs22 last updated on 12/Jan/21 $$\:\mathrm{f}\:'\left(\mathrm{x}\right)=\mathrm{12x}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{4}\right)^{\mathrm{3}} +\mathrm{6x}\left(\mathrm{x}^{\mathrm{2}}…
Question Number 129038 by bramlexs22 last updated on 12/Jan/21 $$\int\:\frac{\mathrm{5e}^{\mathrm{4t}} +\mathrm{10e}^{\mathrm{2t}} +\mathrm{2}}{\mathrm{e}^{\mathrm{2t}} +\mathrm{2}}\:\mathrm{dt}\: \\ $$ Answered by liberty last updated on 12/Jan/21 $$\:\int\:\frac{\left(\mathrm{5e}^{\mathrm{2t}} +\mathrm{1}\right)\left(\mathrm{e}^{\mathrm{2t}} +\mathrm{2}\right)−\mathrm{e}^{\mathrm{2t}}…