Answer:
d. does not exist
Step-by-step explanation:
The given limits are;
[tex]\lim_{x \to 4} f(x) =5[/tex], [tex]\lim_{x \to 4} g(x) =0[/tex] and [tex]\lim_{x \to 4} h(x) =-2[/tex]
We want to find
[tex]\lim_{x \to 4} \frac{f}{g}(x)= \lim_{x \to 4} \frac{f(x)}{g(x)}[/tex]
By the properties of limits, we have;
[tex]\lim_{x \to 4} \frac{f}{g}(x)= \frac{\lim_{x \to 4} f(x)}{\lim_{x \to 4} g(x)}[/tex]
This gives us;
[tex]\lim_{x \to 4} \frac{f}{g}(x)= \frac{5}{0}[/tex]
Division by zero is not possible. Therefore the limit does not exist.
