A

Given the function \(g\) (see the picture), find \(\lim _{x\to \infty }g(x)\). \[ g(x)=\begin{cases} -\frac12(x-1)^2+2 & \text{if } x < 1,\\ \frac2{x^2}+1 & \text{if } x \geq 1 \end{cases} \]

Given the function \(h\) (see the picture), find \(\lim _{x\to 1^{-}}h(x)\). \[ h(x)=\begin{cases} -\frac1{x-1} & \text{if } x< 1,\\ -(x-1)^2+2 & \text{if } x\geq 1 \end{cases} \]

Identify a true statement about the function \(f(x) = \frac{1} {4}x^{4} - x^{3}\).

Given the function \(h\), find \(\lim _{x\to 1^{+}}h(x)\). \[ h(x)=\begin{cases} -\frac1{x-1} & \text{if } x< 1,\\ -(x-1)^2+2 & \text{if } x\geq 1 \end{cases} \]