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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}}…

Question-11341

Question Number 11341 by Nadium last updated on 21/Mar/17 Commented by FilupS last updated on 22/Mar/17 $$\Omega=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{{n}^{\mathrm{4}} }\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\underset{{j}=\mathrm{1}} {\overset{{n}} {\sum}}\left({i}^{\mathrm{2}} +{j}^{\mathrm{2}} \right)\mid{i}^{\mathrm{2}}…

x-x-4-5-x-7-7-x-5-x-

Question Number 142415 by Rankut last updated on 31/May/21 $$\frac{{x}}{{x}+\mathrm{4}}=\frac{\mathrm{5}\lfloor{x}\rfloor−\mathrm{7}}{\mathrm{7}\lfloor{x}\rfloor−\mathrm{5}} \\ $$$${x}=? \\ $$ Answered by mr W last updated on 31/May/21 $${say}\:{x}={n}+{f} \\ $$$$\frac{{n}+{f}}{{n}+{f}+\mathrm{4}}=\frac{\mathrm{5}{n}−\mathrm{7}}{\mathrm{7}{n}−\mathrm{5}}…