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Category: Limits

lim-n-n-1-1-n-1-2-n-1-2n-ln-2-

Question Number 219832 by mnjuly1970 last updated on 02/May/25 $$ \\ $$$$\:\:\:\:\:{lim}_{{n}\rightarrow\infty} \:{n}\left(\frac{\mathrm{1}}{\mathrm{1}+{n}}\:+\frac{\mathrm{1}}{\mathrm{2}+{n}}\:+…+\frac{\mathrm{1}}{\mathrm{2}{n}}\:−{ln}\left(\mathrm{2}\right)\right)=? \\ $$$$ \\ $$ Answered by universe last updated on 03/May/25 Commented…

Question-219731

Question Number 219731 by Nescio last updated on 01/May/25 Answered by breniam last updated on 03/May/25 $$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }×\frac{{x}}{\mathrm{log}\left(\mathrm{1}+\mathrm{2}{x}\right)}×\mathrm{tan}\left({x}\right)={L} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }=\mathrm{1}…

Question-219223

Question Number 219223 by fantastic last updated on 20/Apr/25 Commented by Nicholas666 last updated on 22/Apr/25 https://bekicotsspace.quora.com/How-do-I-solve-the-problem-Let-math-f-x-lim_-n-to-infty-left-frac-n-n-x-n-x-frac-n-2-cdots-x-frac-n?ch=10&oid=220368951&share=05ee32a3&srid=5Xg5SU&target_type=post Answered by zetamaths last updated on 20/Apr/25 $$\frac{{f}'\left(\mathrm{3}\right)}{{f}\left(\mathrm{3}\right)}\geqslant\frac{{f}'\left(\mathrm{2}\right)}{{f}\left(\mathrm{2}\right)}\:\:\:…

4-16-x-2-dx-0-4-16-x-2-dx-0-4-16-x-2-dx-

Question Number 218309 by 200392jjlv last updated on 05/Apr/25 $$\underset{−\infty} {\overset{\infty} {\int}}\frac{\mathrm{4}}{\mathrm{16}+{x}^{\mathrm{2}} }{dx} \\ $$$$=\:\underset{−\infty} {\overset{\mathrm{0}} {\int}}\frac{\mathrm{4}}{\mathrm{16}+{x}^{\mathrm{2}} }{dx}+\underset{\infty} {\int}^{\mathrm{0}} \frac{\mathrm{4}}{\mathrm{16}+{x}^{\mathrm{2}} }{dx} \\ $$$$=\: \\ $$$$…

lim-n-1-n-2n-n-1-n-

Question Number 218196 by mnjuly1970 last updated on 01/Apr/25 $$ \\ $$$$ \\ $$$$\:\:\:\:\mathrm{lim}\:_{\mathrm{n}\rightarrow\infty} \frac{\mathrm{1}}{{n}}\:\left(\:\frac{\left(\mathrm{2}{n}\right)!}{{n}!}\:\right)^{\frac{\mathrm{1}}{{n}}} =\:?\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Answered by mehdee7396 last updated…