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Question Number 27700 by NECx last updated on 13/Jan/18

if f(x)= { ((mx^2 +n,     x<0)),((nx+m,    0≤x≤1)),((nx^3 +m,   x>1)) :}  for what integers m and n does  both lim_(x→0)  f(x) and lim_(x→1) f(x) exist?

$${if}\:{f}\left({x}\right)=\begin{cases}{{mx}^{\mathrm{2}} +{n},\:\:\:\:\:{x}<\mathrm{0}}\\{{nx}+{m},\:\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}}\\{{nx}^{\mathrm{3}} +{m},\:\:\:{x}>\mathrm{1}}\end{cases} \\ $$ $${for}\:{what}\:{integers}\:{m}\:{and}\:{n}\:{does} \\ $$ $${both}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{f}\left({x}\right)\:{and}\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}{f}\left({x}\right)\:{exist}? \\ $$

Commented byNECx last updated on 14/Jan/18

how about this?

$${how}\:{about}\:{this}? \\ $$

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