Question Number 141694 by Dwaipayan Shikari last updated on 22/May/21 $${log}\left(\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{10}}\mathrm{9}{e}^{\gamma} \right)=\frac{\zeta\left(\mathrm{2}\right)}{\mathrm{2}}\left(\frac{\mathrm{1}^{\mathrm{2}} +\mathrm{9}^{\mathrm{2}} }{\mathrm{10}^{\mathrm{2}} }\right)−\frac{\zeta\left(\mathrm{3}\right)}{\mathrm{3}}\:\left(\frac{\mathrm{1}^{\mathrm{3}} +\mathrm{9}^{\mathrm{3}} }{\mathrm{10}^{\mathrm{3}} }\:\right)+\frac{\zeta\left(\mathrm{4}\right)}{\mathrm{4}}\left(\frac{\mathrm{1}^{\mathrm{4}} +\mathrm{9}^{\mathrm{4}} }{\mathrm{10}^{\mathrm{4}} }\right)−… \\ $$$$\gamma={Euler}\:{Mascheroni}\:{Constant} \\ $$…
Question Number 10620 by Saham last updated on 20/Feb/17 Commented by mrW1 last updated on 20/Feb/17 $${please}\:{check}: \\ $$$${after}\:{collision}\:\overset{\rightarrow} {{V}}_{{A}} =−\mathrm{5}.\mathrm{0}{i}+\mathrm{20}{j}\:\:\:\left({not}\:−\mathrm{5}.\mathrm{0}{j}+\mathrm{20}{j}\right) \\ $$$${answer}\:\left({b}\right)\:\mathrm{500}\:{J}\:\:\:\left({not}\:\mathrm{525}\:{J}\right) \\ $$…
Question Number 141691 by mnjuly1970 last updated on 22/May/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….{Calculus}\left({I}\right)…. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}:=\int_{\frac{\mathrm{1}}{\mathrm{2}\:}} ^{\:\mathrm{1}} \frac{\mathrm{1}}{{x}^{\mathrm{2}} \left(\mathrm{1}+{x}^{\mathrm{4}} \right)^{\frac{\mathrm{3}}{\mathrm{4}}} }{dx}=??? \\ $$ Answered by Dwaipayan Shikari last updated…
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Question Number 141685 by mnjuly1970 last updated on 22/May/21 $$\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:……{nice}\:…\:…\:…\:{calculus}….. \\ $$$$\:\:\mathrm{I}{f}\:\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{tan}\left({x}\right)}{{x}}\:=\:\mathrm{1}\:,\:{prove}\:{that}: \\ $$$$\:\:\:\:\:\:\:\:{lim}\frac{\mathrm{1}}{{x}}\left(\frac{\mathrm{1}}{{x}}−\frac{\mathrm{1}}{{tan}\left({x}\right)}\right)=\frac{\mathrm{1}}{\mathrm{3}} \\ $$ Answered by iloveisrael last updated on…
Question Number 76151 by Rio Michael last updated on 24/Dec/19 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}^{{k}} {e}^{−\mathrm{4}{x}} ,\:{k}>\mathrm{0} \\ $$ Commented by kaivan.ahmadi last updated on 24/Dec/19 $${lim}_{{x}−\rightarrow\infty} \frac{{x}^{{k}}…
Question Number 10612 by FilupS last updated on 20/Feb/17 Commented by FilupS last updated on 20/Feb/17 $$\mathrm{Solve}\:\mathrm{for}\:\boldsymbol{{A}}'\:\mathrm{and}\:\boldsymbol{{B}}'\:\mathrm{via}: \\ $$$$\mathrm{1}.\:\:\mathrm{Vectors} \\ $$$$\mathrm{2}.\:\:\mathrm{Triganometry} \\ $$ Answered by…
Question Number 141681 by ZiYangLee last updated on 22/May/21 $$\mathrm{On}\:\mathrm{the}\:\mathrm{Argand}\:\mathrm{Diagram},\:\mathrm{the}\:\mathrm{variable}\:\mathrm{point} \\ $$$$\mathrm{Z}\:\mathrm{represents}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{number}\:{z}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{a}\:\mathrm{point} \\ $$$$\mathrm{Z}\:\mathrm{which}\:\mathrm{moves}\:\mathrm{such}\:\mathrm{that}\:\mid\frac{{z}−\mathrm{1}}{{z}+\mathrm{2}}\mid=\mathrm{2} \\ $$ Answered by MJS_new last updated on 22/May/21…
Question Number 76146 by john santuy last updated on 24/Dec/19 Commented by john santuy last updated on 24/Dec/19 $${how}\:{to}\:{proof}? \\ $$ Commented by mr W…
Question Number 10607 by Saham last updated on 19/Feb/17 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}: \\ $$$$\mathrm{2x}^{\mathrm{3}} \:+\:\mathrm{2x}^{\mathrm{2}} \:−\:\mathrm{5x}\:−\:\mathrm{1}\:=\:\mathrm{0} \\ $$ Answered by mrW1 last updated on 20/Feb/17 $${a}=\mathrm{2} \\…