9000141909

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