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Calculate-the-side-of-an-equilateral-triangle-whose-vertices-are-situated-on-three-parallel-coplanar-lines-knowing-that-a-and-b-are-the-distances-of-the-parallel-line-to-the-others-

Question Number 76974 by Maclaurin Stickker last updated on 02/Jan/20 $${Calculate}\:{the}\:{side}\:{of}\:{an}\:{equilateral} \\ $$$${triangle}\:{whose}\:{vertices}\:{are}\:{situated} \\ $$$${on}\:{three}\:{parallel}\:{coplanar}\:{lines}, \\ $$$${knowing}\:{that}\:\boldsymbol{{a}}\:{and}\:\boldsymbol{{b}}\:{are}\:{the}\:{distances} \\ $$$${of}\:{the}\:{parallel}\:{line}\:{to}\:{the}\:{others}. \\ $$ Answered by mr W…

F-x-x-x-2-1-ln-t-dt-Show-that-F-x-x-2-x-ln-x-Please-

Question Number 142443 by Hassen_Timol last updated on 31/May/21 $$\:\:\:\:\:\:{F}\left({x}\right)\:=\:\int_{\:{x}} ^{\:\:{x}^{\mathrm{2}} } \frac{\mathrm{1}}{\:\mathrm{ln}\left({t}\right)\:}\:\mathrm{d}{t} \\ $$$$\:\:\mathrm{Show}\:\mathrm{that}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mid\:{F}\left({x}\right)\:\mid\:\:\leqslant\:\:\frac{\mid\:{x}^{\mathrm{2}} \:−\:{x}\:\mid}{\mid\:\mathrm{ln}\left({x}\right)\:\mid} \\ $$$$ \\ $$$$\mathrm{Please} \\ $$ Answered…

Question-142437

Question Number 142437 by mohammad17 last updated on 31/May/21 Answered by Dwaipayan Shikari last updated on 31/May/21 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{{n}}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\sqrt{\frac{{n}}{{n}+{r}}}\: \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}}}{dx}\:\:\:\:\mathrm{1}+{x}={u}^{\mathrm{2}}…