Question Number 4118 by Filup last updated on 29/Dec/15
$$\mathrm{Does}\:\mathrm{a}\:\mathrm{function}\:{f}\left({x}\right)\:\mathrm{exist} \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{for} \\ $$$${f}^{\:\left({n}\right)} \left({x}\right)=\frac{{d}^{{n}} {f}}{{dx}^{{n}} } \\ $$$$\mathrm{That}: \\ $$$$\left(\mathrm{1}\right)\:\:\:\:\:\underset{{n}\rightarrow{k}} {\mathrm{lim}}\:{f}^{\:\left({n}\right)} \left({x}\right)={k} \\ $$$$\boldsymbol{\mathrm{and}} \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:\underset{{n}\rightarrow{k}} {\mathrm{lim}}\:{f}^{\:\left({n}\right)} \left({x}\right)={f}\left({k}\right) \\ $$
Commented by prakash jain last updated on 29/Dec/15
$$\underset{{n}\rightarrow{k}} {\mathrm{lim}}\:{f}^{\left({n}\right)} \left({x}\right)={k}={f}\left({k}\right)? \\ $$
Commented by prakash jain last updated on 29/Dec/15
$$\mathrm{Either}\:{f}\left({k}\right)={k}\:\mathrm{or}\:\mathrm{limit}\:\mathrm{does}\:\mathrm{not}\:\mathrm{exist}. \\ $$