Given that
$$\lim_{x \to 1} f(x) = 5, \lim_{x \to 1} g(x) = -2, \lim_{x \to 1} h(x) = 1,$$
determine the following limits. Give an exact answer if a limit is a number. Otherwise, enter $-\infty$ or $\infty$ if a limit is infinite, or enter DNE if a limit does not exist in another way.
a. $\lim_{x \to 1} 2f(x)g(x) =$
b. $\lim_{x \to 1} \frac{g(x)-1}{f(x)} =$
c. $\lim_{x \to 1} f(x) + \frac{1}{3}g(x) =$
d. $\lim_{x \to 1} \frac{h(x)^3}{2} =$
e. $\lim_{x \to 1} xh(x) =$
