Question Number 219733 by Spillover last updated on 01/May/25
Answered by SdC355 last updated on 01/May/25
$$\mid\mathrm{g}\left({x}\right)−\mathrm{2}\mid\leq\mathrm{3}\left({x}−\mathrm{1}\right)^{\mathrm{2}} \\ $$$$−\mathrm{3}\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{2}\leq\mathrm{g}\left({x}\right)\leq\mathrm{3}\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{2} \\ $$$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}−\mathrm{3}\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{2}\leq\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\mathrm{g}\left({x}\right)\leq\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\mathrm{3}\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{2} \\ $$$$\mathrm{2}\leq\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\mathrm{g}\left({x}\right)\leq\mathrm{2}\: \\ $$$$\therefore\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\mathrm{g}\left({x}\right)=\mathrm{2}\: \\ $$
Commented by Spillover last updated on 01/May/25
$${thank}\:{you} \\ $$
Answered by Spillover last updated on 01/May/25
