Diketahui lim x->2 g(x)=9 dan lim x->2 f(x)=4. Hitunglah:

a. 5, b. 3/2

Pembahasan

Diketahui $\lim_{x \to 2} g(x) = 9$ dan $\lim_{x \to 2} f(x) = 4$. 
a. $\lim_{x \to 2} [g(x) - f(x)] = \lim_{x \to 2} g(x) - \lim_{x \to 2} f(x) = 9 - 4 = 5$. 
b. $\lim_{x \to 2} \sqrt{\frac{g(x)}{f(x)}} = \sqrt{\frac{\lim_{x \to 2} g(x)}{\lim_{x \to 2} f(x)}} = \sqrt{\frac{9}{4}} = \frac{3}{2}$.