Question Number 135638 by Dwaipayan Shikari last updated on 14/Mar/21 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\sqrt{\mathrm{5}}−\mathrm{2}\right)^{\mathrm{2}{n}+\mathrm{1}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }=\frac{\pi^{\mathrm{2}} }{\mathrm{24}}−\frac{\mathrm{1}}{\mathrm{12}}{log}^{\mathrm{2}} \left(\mathrm{2}+\sqrt{\mathrm{5}}\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 135633 by metamorfose last updated on 14/Mar/21 $$\int\frac{\mathrm{1}}{{x}^{\frac{\mathrm{1}}{\mathrm{3}}} +\mathrm{1}}{dx}=…? \\ $$ Answered by Ñï= last updated on 14/Mar/21 $$\int\frac{{dx}}{{x}^{\frac{\mathrm{1}}{\mathrm{3}}} +\mathrm{1}}\overset{{t}={x}^{\frac{\mathrm{1}}{\mathrm{3}}} } {=}\int\frac{\mathrm{3}{t}^{\mathrm{2}} {dt}}{{t}+\mathrm{1}}=\mathrm{3}\int\frac{\left({t}+\mathrm{1}\right)\left({t}−\mathrm{1}\right)+\mathrm{1}}{{t}+\mathrm{1}}{dt}=\mathrm{3}\int\left\{\left({t}−\mathrm{1}\right)+\frac{\mathrm{1}}{{t}+\mathrm{1}}\right\}{dt}…
Question Number 135635 by mohammad17 last updated on 14/Mar/21 Commented by mohammad17 last updated on 14/Mar/21 $${help}\:{me}\:{sir}\: \\ $$ Answered by Olaf last updated on…
Question Number 135634 by oustmuchiya@gmail.com last updated on 14/Mar/21 Answered by physicstutes last updated on 14/Mar/21 $$\left({i}\right)\:{n}\left({B}\right)\:=\:\mathrm{8}\:+\:\mathrm{5}\:+\:{x}−\mathrm{4}\:=\:\mathrm{11}\:+\:{x} \\ $$$$\:{n}\left(\:{B}\cup{C}\right)\:=\:\mathrm{8}+\:{x}−\mathrm{4}\:+\:\mathrm{5}\:+\:\mathrm{2}{y}\:=\:\mathrm{9}\:+\:{x}\:+\:\mathrm{2}{y} \\ $$$$\Rightarrow\:\:\mathrm{11}\:+\:{x}\:=\:\mathrm{9}\:+{x}\:+\:\mathrm{2}{y}\:\:\Rightarrow\:\:\:\mathrm{2}\:=\:\mathrm{2}{y}\:\Rightarrow\:{y}\:=\:\mathrm{1} \\ $$$$\left({ii}\right)\:{n}\left({C}\right)\:=\:\mathrm{5}\:+\:\mathrm{2}{y}\: \\ $$$$\mathrm{and}\:{n}\left({A}\right)\:=\:\mathrm{15}…
Question Number 135629 by Ñï= last updated on 14/Mar/21 $$\underset{{xlnx}\rightarrow\mathrm{1}} {\mathrm{lim}}\left(\frac{{xlnlnx}+\mathrm{1}}{{x}−{e}^{\frac{\mathrm{1}}{{x}}} }−{x}\right)=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 4559 by love math last updated on 07/Feb/16 $$\left(\mathrm{0};\left(\mathrm{4}\right)\right)^{{x}^{\mathrm{2}} −\mathrm{1}} >\left(\mathrm{0},\left(\mathrm{6}\right)\right)^{{x}^{\mathrm{2}} +\mathrm{6}} \\ $$ Commented by Yozzii last updated on 07/Feb/16 $${What}\:{is}\:\left(\mathrm{0},\left(\mathrm{6}\right)\right)\:{and}\:\left(\mathrm{0};\left(\mathrm{4}\right)\right)? \\…
Question Number 135630 by rexford last updated on 14/Mar/21 Answered by mr W last updated on 14/Mar/21 Commented by mr W last updated on 14/Mar/21…
Question Number 4556 by FilupSmith last updated on 07/Feb/16 $$\mathrm{Prove}\:{i}^{{i}} ={e}^{−\pi/\mathrm{2}} ,\:\:{i}^{\mathrm{2}} =−\mathrm{1} \\ $$ Answered by Yozzii last updated on 07/Feb/16 $${i}=\mathrm{0}+{i}×\mathrm{1}={cos}\mathrm{0}.\mathrm{5}\pi+{isin}\mathrm{0}.\mathrm{5}={e}^{\mathrm{0}.\mathrm{5}\pi{i}} \\ $$$$\therefore{i}^{{i}}…
Question Number 4555 by FilupSmith last updated on 07/Feb/16 $${y}={x}^{{i}} \\ $$$${x}\in\mathbb{R} \\ $$$${i}^{\mathrm{2}} =−\mathrm{1} \\ $$$$ \\ $$$$\mathrm{is}\:{y}\in\mathbb{C}? \\ $$ Commented by Yozzii last…
Question Number 135624 by liberty last updated on 14/Mar/21 $$ \\ $$A polynomial p(x) leaves a remainder of -1 when divided by x – 1,…