For a function

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

Problem

For a function ff, which of the following guarantees that lim⁡x→cf(x)\displaystyle \lim_{x\to c}f(x) exists and equals a finite value LL? (a) lim⁡x→c−f(x)=f(c)=L\displaystyle \lim_{x\to c^-}f(x)=f(c)=L (b) lim⁡x→c−f(x)=lim⁡x→c+f(x)=∞\displaystyle \lim_{x\to c^-}f(x)=\lim_{x\to c^+}f(x)=\infty (c) lim⁡x→c−f(x)=lim⁡x→c+f(x)=L\displaystyle \lim_{x\to c^-}f(x)=\lim_{x\to c^+}f(x)=L (d) lim⁡x→c−f(x)=lim⁡x→c+f(x)\displaystyle \lim_{x\to c^-}f(x)=\lim_{x\to c^+}f(x)

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