Determine the behavior of the functions defined below. If a limit does not exist or the function is undefined, write DNE.\na. Consider $h(x) = \frac{4x^3 + 7x^2}{-x^3 + 7x}$. \ni. For what value(s) of $x$ is $h(x)$ undefined?\n$x = \sqrt{7}, -\sqrt{7}$ \nii. For what value(s) of $x$ does $h(x)$ have a vertical asymptote?\n$x = \sqrt{7}, -\sqrt{7}$ \niii. For what value(s) of $x$ does $h(x)$ have a hole?\n$x = 0$ \niv. $\lim_{x \to 0} h(x) = 0$ \nv. $\lim_{x \to \infty} h(x) = -4$ \nvi. $\lim_{x \to -\infty} h(x) = -4$ \nb. Based on your work in part a, on what interval(s) is $h(x)$ continuous? $( -\infty, -\sqrt{7}) \cup (-\sqrt{7}, 0) \cup (0, \infty)$ \nWrite your answer in interval notation. If you include multiple intervals, use u to denote union.