Which one of the following is the necessary and sufficient condition for the limit to…

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

Problem

Which one of the following is the necessary and sufficient condition for the limit lim⁡x→af(x)\displaystyle \lim_{x\to a}f(x) to exist and equal LL? (a) f(a)=Lf(a)=L (b) Both lim⁡x→a−f(x)\displaystyle \lim_{x\to a^-}f(x) and lim⁡x→a+f(x)\displaystyle \lim_{x\to a^+}f(x) exist and are equal to LL (c) Either lim⁡x→a−f(x)\displaystyle \lim_{x\to a^-}f(x) or lim⁡x→a+f(x)\displaystyle \lim_{x\to a^+}f(x) equals LL (d) lim⁡x→a−f(x)=lim⁡x→a+f(x)\displaystyle \lim_{x\to a^-}f(x)=\lim_{x\to a^+}f(x)

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