Question Number 63351 by aliesam last updated on 02/Jul/19 Commented by mathmax by abdo last updated on 03/Jul/19 $${let}\:{I}\:=\int\:\:\:\frac{{dx}}{\mathrm{4}+\left({x}−\mathrm{3}\right)^{\mathrm{2}} }\:\:\:{changement}\:\:{x}−\mathrm{3}\:=\mathrm{2}{t}\:{give} \\ $$$${I}\:=\:\int\:\:\frac{\mathrm{2}{dt}}{\mathrm{4}+\mathrm{4}{t}^{\mathrm{2}} }\:=\:\int\:\:\:\:\frac{{dt}}{\mathrm{2}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}\:=\frac{\mathrm{1}}{\mathrm{2}}\:{arctan}\left({t}\right)+{c} \\…
Question Number 128885 by naka3546 last updated on 11/Jan/21 $${e}^{{e}^{{x}} } \:=\:{x} \\ $$$${x}\:=\:? \\ $$ Commented by naka3546 last updated on 11/Jan/21 $${x}\:\in\:\mathbb{R}\:?\:{or}\:{x}\:\in\:\mathbb{C}\:? \\…
Question Number 128874 by help last updated on 11/Jan/21 Commented by Ritu Jain last updated on 11/Jan/21 $$\mathrm{18} \\ $$ Answered by Olaf last updated…
Question Number 63336 by ajfour last updated on 02/Jul/19 Commented by ajfour last updated on 02/Jul/19 $${Find}\:{the}\:{equation}\:{of}\:{the}\:{parabola} \\ $$$${in}\:{the}\:{form}:\:\:\:{y}={Ax}^{\mathrm{2}} +{C}\:. \\ $$ Answered by mr…
Question Number 63324 by pradyot_pathak last updated on 02/Jul/19 Answered by Hope last updated on 02/Jul/19 $${area}\:{of}\:{pentagon}=\frac{\mathrm{1}}{\mathrm{4}}×\mathrm{5}×\mathrm{12}^{\mathrm{2}} ×{cot}\left(\frac{\mathrm{180}^{{o}} }{\mathrm{5}}\right) \\ $$$$=\mathrm{180}×{cot}\mathrm{36}^{{o}} \\ $$$${external}\:{angle}=\frac{\mathrm{360}^{{o}} }{\mathrm{5}}=\mathrm{72}^{{o}} \\…
Question Number 128853 by Ar Brandon last updated on 10/Jan/21 $$\mathrm{F}\left(\mathrm{x}\right)=\int_{\mathrm{x}} ^{\mathrm{2x}} \frac{\mathrm{dx}}{\:\sqrt{\mathrm{t}^{\mathrm{4}} +\mathrm{t}^{\mathrm{2}} +\mathrm{1}}} \\ $$$$\mathrm{1}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{F}\:\mathrm{is}\:\mathrm{defined},\:\mathrm{continuous}\:\mathrm{and}\:\mathrm{derivable}\:\mathrm{in}\:\mathbb{R} \\ $$ Answered by mathmax by abdo last…
Question Number 128850 by ruwedkabeh last updated on 10/Jan/21 $$\sqrt{{x}+\sqrt{\mathrm{4}{x}+\sqrt{\mathrm{16}{x}+\sqrt{\mathrm{64}{x}+…+\sqrt{\mathrm{4}^{\mathrm{2019}} {x}+\mathrm{3}}}}}}−\sqrt{{x}}=\mathrm{1} \\ $$$${x}=? \\ $$ Answered by mindispower last updated on 10/Jan/21 $$\Rightarrow\sqrt{\mathrm{4}{x}+……+\sqrt{\mathrm{4}^{\mathrm{2009}} {x}+\mathrm{3}}}=\mathrm{1}+\mathrm{2}\sqrt{{x}} \\…
Question Number 128851 by mnjuly1970 last updated on 10/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:\:{calculus}\:\:\left({I}\right)… \\ $$$$\:\:\:{calculate}\:\::: \\ $$$$ \\ $$$$\:\:\:\:\:\Psi=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left\{\left({e}−\mathrm{1}\right)\sqrt{{log}\left(\:\mathrm{1}+{ex}−{x}\:\right)}\:+{e}^{{x}^{\mathrm{2}} } \right\}{dx}=? \\ $$$$ \\ $$ Commented…
Question Number 128849 by I want to learn more last updated on 10/Jan/21 Commented by Tawa11 last updated on 15/Sep/21 $$\mathrm{nice} \\ $$ Answered by…
Question Number 128846 by Ar Brandon last updated on 10/Jan/21 $$\mathrm{u}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{sin}\left(\frac{\mathrm{k}\pi}{\mathrm{n}}\right)\mathrm{sin}\left(\frac{\mathrm{k}}{\mathrm{n}^{\mathrm{2}} }\right) \\ $$$$\mathrm{Find}\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}u}_{\mathrm{n}} \\ $$ Commented by Dwaipayan Shikari last…