Question Number 65319 by hovea cw last updated on 28/Jul/19 Commented by mathmax by abdo last updated on 28/Jul/19 $${those}\:{integrals}\:{are}\:{solved}\:\:{see}\:{the}\:{platform}. \\ $$ Commented by mathmax…
Question Number 130852 by Algoritm last updated on 29/Jan/21 Answered by Dwaipayan Shikari last updated on 29/Jan/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−{cos}\frac{{x}}{\mathrm{2}}}{{x}^{\mathrm{2}} }=\mathrm{2}\left(\frac{{sin}^{\mathrm{2}} \frac{{x}}{\mathrm{4}}}{{x}^{\mathrm{2}} }\right)=\frac{\mathrm{2}}{\mathrm{16}}=\frac{\mathrm{1}}{\mathrm{8}} \\ $$ Answered…
Question Number 130853 by Koyoooo last updated on 29/Jan/21 Answered by mathmax by abdo last updated on 29/Jan/21 $$\mathrm{for}\:\mathrm{x}\in\mathrm{C}\:\:\:\:\mathrm{no}\:\mathrm{difference}\:\:\sqrt{\mathrm{x}^{\mathrm{2}} }=\left(\sqrt{\mathrm{x}}\right)^{\mathrm{2}} \\ $$$$\mathrm{inside}\:\mathrm{R}\:\:\sqrt{\mathrm{x}^{\mathrm{2}} }=\mid\mathrm{x}\mid\:\mathrm{here}\:\mathrm{x}\:\in\mathrm{R}\:\:\mathrm{and}\:\left(\sqrt{\mathrm{x}}\right)^{\mathrm{2}} \:=\mathrm{x}\:\mathrm{here}\:\mathrm{x}\in\mathrm{R}^{+} \\…
Question Number 65314 by Tony Lin last updated on 28/Jul/19 Commented by Tony Lin last updated on 28/Jul/19 $${prove}\:{that}\:\frac{\mathrm{1}}{{GM}}−\frac{\mathrm{1}}{{HM}}=\frac{\mathrm{1}}{{AM}}−\frac{\mathrm{1}}{{BM}} \\ $$ Terms of Service Privacy…
Question Number 130849 by TITA last updated on 29/Jan/21 Commented by Ñï= last updated on 29/Jan/21 Answered by EDWIN88 last updated on 30/Jan/21 $$−\mathrm{2}{y}=−\mathrm{2}{a}\mathrm{cos}\:\mathrm{2}{x}−\mathrm{2}{b}\mathrm{sin}\:\mathrm{2}{x} \\…
Question Number 65312 by Tony Lin last updated on 28/Jul/19 Commented by Tony Lin last updated on 28/Jul/19 $${how}\:{to}\:{know}\:{x}=\mathrm{5} \\ $$ Commented by mr W…
Question Number 130846 by Eric002 last updated on 29/Jan/21 $${prove}\:{that} \\ $$$$\mathrm{3}{sec}^{−\mathrm{1}} \left(\sqrt{\mathrm{2}}\right)−\mathrm{4}{csc}^{−\mathrm{1}} \left(\sqrt{\mathrm{2}}\right)+\mathrm{5}{cot}^{−\mathrm{1}} \left(\mathrm{2}\right)=\mathrm{1}.\mathrm{533} \\ $$ Commented by MJS_new last updated on 30/Jan/21 $$\mathrm{we}\:\mathrm{cannot}\:\mathrm{prove}\:\mathrm{this}\:\mathrm{as}\:\mathrm{it}\:\mathrm{is}\:\mathrm{not}\:\mathrm{true}…
Question Number 130844 by mnjuly1970 last updated on 29/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:\:\:{advanced}\:\:\:{calculus}… \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{3}}} \frac{{dx}}{\:\sqrt[{\mathrm{3}}]{{cos}^{\mathrm{2}} \left({x}\right)}}\:=\frac{\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{3}}} \sqrt{\pi}}{\:\sqrt{\mathrm{3}}} \\ $$ Answered by Dwaipayan Shikari last…
Question Number 130845 by mnjuly1970 last updated on 29/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:…\:\:{nice}\:\:{calculus}… \\ $$$$\:\:{calculate}:: \\ $$$$\:\:\:{lim}_{\:{n}\rightarrow\infty} \underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{k}}{\mathrm{2}{n}^{\mathrm{2}} +{k}}\:=? \\ $$$$ \\ $$ Answered by Ar…
Question Number 65307 by divyajyoti last updated on 28/Jul/19 $$\int\frac{\left(\mathrm{4}{x}+\mathrm{3}\right){dx}}{\:\sqrt{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{3}}}\:=\:?\: \\ $$ Answered by divyajyoti last updated on 28/Jul/19 $$=\int\frac{{dt}}{\:\sqrt{{t}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\int\frac{{dx}}{\:\sqrt{\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} −\left(\frac{\sqrt{\mathrm{7}}}{\mathrm{2}}\right)^{\mathrm{2}} }} \\ $$$$=\mathrm{2}\sqrt{\mathrm{2}{x}^{\mathrm{2}}…