Category: Differentiation

Question Number 216800 by depressiveshrek last updated on 21/Feb/25 Answered by MrGaster last updated on 21/Feb/25 $$\mathrm{Prove}:{f}\left({x}\right)={a}\left({x}−{r}_{\mathrm{1}} \right)^{{m}_{\mathrm{1}} } \left({x}−{r}_{\mathrm{2}} \right)^{{m}_{\mathrm{2}} } \ldots\left({x}−{r}_{{k}} \right)^{{m}_{{k}} }…

Question Number 216638 by Nadirhashim last updated on 13/Feb/25 $$\mathit{w}\mathit{i}\mathit{t}\mathit{h}\mathit{o}\mathit{u}\mathit{t}\mathit{u}\mathit{s}\mathit{i}\mathit{n}\mathit{g}\mathit{L}\mathit{H}\mathit{o}\mathit{p}\mathit{i}\mathit{t}\mathit{a}\mathit{l}$$$$\mathit{r}\mathit{u}\mathit{l}\mathit{e}\mathit{e}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{t}\mathit{e}$$$$\underset{x\to 0}{\lim }\frac{\mathit{l}\mathit{n}(1-x)-\mathit{s}\mathit{i}\mathit{n}\left(\mathit{x}\right)}{1-{\mathit{c}\mathit{o}\mathit{x}}^2\left(\mathit{x}\right)}$$ Commented by MathematicalUser2357 last updated on 13/Feb/25…

Question Number 215979 by alcohol last updated on 23/Jan/25 $$u_n=\underset{k=n+1}{\sum ^{2n}}\frac{1}{k}and{v}_n=\underset{k=n}{\sum ^{2n-1}}\frac{1}{k}$$$$\bullet showthat{u}_{n}and{v}_{n}areadjacent$$$$useln(x+1)⩽xandx⩽-ln(1-x)and$$$$\bullet\:{show}\:{that}\:{u}_{{n}} \:\leqslant\:\underset{{k}={n}+\mathrm{1}}…

Question Number 215958 by Tawa11 last updated on 22/Jan/25 $$\mathrm{Find}\mathrm{the}\mathrm{only}\mathrm{function}\mathrm{that}\mathrm{satisfy}$$$$\mathrm{the}\mathrm{expression}\mathrm{below}:$$$${\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^2=\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2}$$ Answered by Ghisom last updated on…

Question Number 215528 by alephnull last updated on 09/Jan/25 Commented by mr W last updated on 10/Jan/25 $$thisisnotaquestion,actuallypure$$$$non-sensewithalotof$$$$mathematicalsymbolsstacked$$$${together}. \…