Which of the following equalities is necessary and sufficient for a function to be…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Which of the following equalities is necessary and sufficient for a function ff to be continuous at x=ax=a? (a) lim⁡x→a−f(x)=lim⁡x→a+f(x)\displaystyle \lim_{x\to a^-}f(x)=\lim_{x\to a^+}f(x) (b) lim⁡x→a+f(x)=f(a)\displaystyle \lim_{x\to a^+}f(x)=f(a) (c) lim⁡x→a−f(x)=lim⁡x→a+f(x)=f(a)\displaystyle \lim_{x\to a^-}f(x)=\lim_{x\to a^+}f(x)=f(a) (d) lim⁡h→0f(a+h)−f(a)h=0\displaystyle \lim_{h\to 0}\frac{f(a+h)-f(a)}{h}=0

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