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Author: Tinku Tara

x-x-30-2-1-2-

Question Number 142730 by Gbenga last updated on 04/Jun/21 $${x}^{{x}^{\mathrm{30}} } =\sqrt{}\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$ Commented by mr W last updated on 04/Jun/21 $${x}=\sqrt[{\mathrm{30}}]{\frac{\mathrm{15ln}\:\mathrm{2}}{\mathrm{2}{W}\left(\frac{\mathrm{15ln}\:\mathrm{2}}{\mathrm{2}}\right)}}\approx\mathrm{1}.\mathrm{045993524} \\ $$…

0-pi-2-sin-2t-1-xsin-2t-dt-

Question Number 142724 by lapache last updated on 04/Jun/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{sin}\left(\mathrm{2}{t}\right)}{\mathrm{1}+{xsin}\left(\mathrm{2}{t}\right)}{dt}=…. \\ $$ Answered by Ar Brandon last updated on 04/Jun/21 $$\mathrm{I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin2t}}{\mathrm{1}+\mathrm{xsin2t}}\mathrm{dt}=\frac{\mathrm{1}}{\mathrm{x}}\int_{\mathrm{0}}…

lim-x-0-x-1-cos-x-

Question Number 142721 by mathlove last updated on 04/Jun/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}}{\:\sqrt{\mathrm{1}−\mathrm{cos}\:{x}}}=? \\ $$ Answered by Ar Brandon last updated on 04/Jun/21 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{x}}{\:\sqrt{\mathrm{1}−\mathrm{cosx}}}=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{x}}{\:\sqrt{\mathrm{1}−\left(\mathrm{1}−\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}\right)}}=\underset{\mathrm{x}\rightarrow\mathrm{0}}…

given-3-y-1-6-2-x-3-y-x-2-find-1-x-1-y-

Question Number 77186 by jagoll last updated on 04/Jan/20 $$\mathrm{given}\: \\ $$$$\begin{cases}{\mathrm{3}^{\mathrm{y}} −\mathrm{1}=\:\frac{\mathrm{6}}{\mathrm{2}^{\mathrm{x}} }}\\{\left(\mathrm{3}\right)^{\frac{\mathrm{y}}{\mathrm{x}}} \:=\:\mathrm{2}\:}\end{cases}\:\:\mathrm{find}\:\frac{\mathrm{1}}{\mathrm{x}}+\frac{\mathrm{1}}{\mathrm{y}}. \\ $$ Answered by john santu last updated on 04/Jan/20…

discrete-mathematics-prove-that-n-1-1-F-2n-1-1-5-5-2-F-n-fibonacci-sequence-

Question Number 142723 by mnjuly1970 last updated on 04/Jun/21 $$\:\:\:\:\:\:\:\:…….\:{discrete}\:\:…..\:\:{mathematics}……. \\ $$$$\:\:\:\:{prove}\:{that}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{F}_{\mathrm{2}{n}+\mathrm{1}} −\mathrm{1}}\overset{?} {=}\frac{\mathrm{5}−\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:{F}_{{n}} \:::\:{fibonacci}\:\:{sequence}… \\ $$ Answered by…