9000141906

Given the function $g$ (see the picture), find $\underset{x\to \mathrm{\infty }}{lim}g(x)$. $$g(x)=\{\begin{array}{ll}-\frac{1}{2}(x-1{)}^2+2& \text{if }x<1,\\ \frac{2}{x^2}+1& \text{if }x\ge 1\end{array}$$