When evaluating the quotient limit by direct substitution

MATHEMATICS · Single correct · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

When evaluating the quotient limit

\displaystyle \lim_{x\to a}\frac{f(x)}{g(x)}

by direct substitution, which of the following conditions must be satisfied in order to guarantee that the limit equals

\dfrac{L}{M}

, where

L=\lim_{x\to a}f(x)

and

M=\lim_{x\to a}g(x)

? (a)

L=0

(b) Both

f

and

g

are continuous at

x=a

(c)

M\neq 0

(d) Both

L

and

M

are finite