Answer to Question #274133 in Real Analysis for teddy

Question

If lim f(x) and lim g(x) exist as x approaches a then lim [ f(x) / g(x) ] = lim f(x) / lim g(x) as x approaches a. true or false

Answer 1

False.

Correct statement

If lim $\lim f(x)$ and $\lim g(x)$ exist as $x$ approaches $a$ then

$$\lim\limits_{x\to a}\dfrac{f(x)}{g(x)}=\dfrac{\lim\limits_{x\to a}f(x)}{\lim\limits_{x\to a}g(x)}\text{ if }\lim\limits_{x\to a}g(x)\not=0$$