Suppose and . Is the limit necessarily defined and finite? Give a brief reason for…

MATHEMATICS · Subjective · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

Suppose

\displaystyle \lim_{x\to 2} f(x)=3

and

\displaystyle \lim_{x\to 2} g(x)=0

. Is the limit

\displaystyle \lim_{x\to 2}\dfrac{f(x)}{g(x)}

necessarily defined and finite? Give a brief reason for your answer.