Suppose-that-f-and-g-are-two-functions-such-that-lim-x-a-g-x-0-and-lim-x-a-f-x-g-x-exist-Prove-that-lim-x-a-f-x-0-

Question Number 42933 by Joel578 last updated on 05/Sep/18

Suppose that f and g are two functions such that

\lim_{x \to a} g (x) = 0 and \lim_{x \to a} \frac{f (x)}{g (x)} exist .

Prove that \lim_{x \to a} f (x) = 0

Commented by MrW3 last updated on 05/Sep/18

h (x) = \frac{f (x)}{g (x)}

\Rightarrow f (x) = h (x) g (x)

\lim_{x \to a} f (x) = \lim_{x \to a} h (x) \times \lim_{x \to a} g (x) = b \times 0 = 0

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