Question Number 27700 by NECx last updated on 13/Jan/18
$${if}\:{f}\left({x}\right)=\begin{cases}{{mx}^{\mathrm{2}} +{n},\:\:\:\:\:{x}<\mathrm{0}}\\{{nx}+{m},\:\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}}\\{{nx}^{\mathrm{3}} +{m},\:\:\:{x}>\mathrm{1}}\end{cases} \\ $$$${for}\:{what}\:{integers}\:{m}\:{and}\:{n}\:{does} \\ $$$${both}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{f}\left({x}\right)\:{and}\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}{f}\left({x}\right)\:{exist}? \\ $$
Commented by NECx last updated on 14/Jan/18
$${how}\:{about}\:{this}? \\ $$