Menu Close

Category: Limits

Question-203668

Question Number 203668 by Perelman last updated on 25/Jan/24 Answered by witcher3 last updated on 25/Jan/24 xf143xf(x)=3(43x)2x[1,13]f(x)[17,13]..(1)$$\left.\Rightarrow\mathrm{f}\left[−\mathrm{1},\frac{\mathrm{1}}{\mathrm{3}}\right]\right)\subset\left[\frac{\mathrm{1}}{\mathrm{7}},\frac{\mathrm{1}}{\mathrm{3}}\right]…

Question-203059

Question Number 203059 by hassanmpsy last updated on 08/Jan/24 Commented by witcher3 last updated on 11/Jan/24 $$\mathrm{U}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{n}\left(\mathrm{1}+\frac{\mathrm{k}}{\mathrm{n}}\right)}{\mathrm{n}^{\mathrm{2}} \left(\mathrm{2}+\mathrm{2}\frac{\mathrm{k}}{\mathrm{n}}+\left(\frac{\mathrm{k}}{\mathrm{n}}\right)^{\mathrm{2}} \right)}=\frac{\mathrm{1}}{\mathrm{n}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{f}\left(\frac{\mathrm{k}}{\mathrm{n}}\right) \

Question-202530

Question Number 202530 by Calculusboy last updated on 28/Dec/23 Answered by MathematicalUser2357 last updated on 29/Dec/23 =limx0log(1+x)1+xxx2$$=\frac{\mathrm{1}}{\mathrm{2}}\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\partial^{\mathrm{2}} }{\partial^{\mathrm{2}} {x}}\left(\mathrm{log}\left(\mathrm{1}+{x}\right)^{\mathrm{1}+{x}}…