We have been given that [tex]\lim_{x \to a} f(x)=5[/tex], [tex]\lim_{x \to a} g(x)=0[/tex] and [tex]\lim_{x \to a} h(x)=-2[/tex]. We are asked to find the [tex]\lim_{x \to a} \frac{g}{h}(x)[/tex].
We will use limit rules to solve our given problem.
[tex]\lim_{x \to a} \frac{g}{h}(x)=\lim_{x \to a} \frac{g(x)}{h(x)}= \frac{\lim_{x \to a}g(x)}{\lim_{x \to a}h(x)}[/tex]
Upon substituting our given values in above formula, we will get:
[tex]\frac{\lim_{x \to a}g(x)}{\lim_{x \to a}h(x)}=\frac{0}{-2}[/tex]
[tex]\frac{\lim_{x \to a}g(x)}{\lim_{x \to a}h(x)}=0[/tex]
Therefore, [tex]\lim_{x \to a} \frac{g}{h}(x)[/tex] is 0 and option C is the correct choice.
