For a function

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

Problem

For a function

f

, it is known that

\displaystyle \lim_{x\to a^-}f(x)=2

and

\displaystyle \lim_{x\to a^+}f(x)=5

. Which statement is necessarily true? (a)

f

is continuous at

x=a

(b)

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

does not exist because the one–sided limits are unequal (c)

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

exists and equals

2

(d)

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

exists and equals

5