Category: Limits

Question Number 163042 by qaz last updated on 03/Jan/22 $$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\sqrt{\mathrm{n}}{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{\cos \mathrm{x}}{{(1+{\mathrm{x}}^2)}^{\mathrm{n}}}\mathrm{dx}=?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 163039 by qaz last updated on 03/Jan/22 $$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\sqrt{\mathrm{n}}{\int }_0^1\mathrm{x}\cdot {\sin }^{2\mathrm{n}}\left(2\pi \mathrm{x}\right)\mathrm{dx}=?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 162925 by qaz last updated on 02/Jan/22 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{4}} }\left[\left(\mathrm{1}+\mathrm{x}+\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}+\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{3}}\right)^{\frac{\mathrm{1}}{\mathrm{x}+\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}+\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{3}}}} −\left(\mathrm{1}+\mathrm{x}+\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}+\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{3}}+\frac{\mathrm{x}^{\mathrm{4}} }{\mathrm{4}}\right)^{\frac{\mathrm{1}}{\mathrm{x}+\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}+\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{3}}+\frac{\mathrm{x}^{\mathrm{4}} }{\mathrm{4}}}} \right]=? \…

Question Number 97355 by bagjamath last updated on 07/Jun/20 Commented by PRITHWISH SEN 2 last updated on 07/Jun/20 $$=\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }(\frac{\pi }{\mathrm{n}+1}+\frac{\pi }{\mathrm{n}+1}+\dots \dots +\frac{\pi }{\mathrm{n}+1}\mathrm{ntimes})$$$$=\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\frac{\pi }{1+\frac{1}{\mathrm{n}}}=\pi$$…

Question Number 31709 by gunawan last updated on 13/Mar/18 $$\mathrm{Given}\mathrm{sequence}\left(y_n\right)\mathrm{with}{y}_1=1,$$$$y_{n+1}=\frac{1}{4}(y_n^3+y_n^2)-1$$$$\mathrm{find}\underset{x\to \mathrm{\infty }}{\lim }{y}_n$$ Terms…