Mathematics

Mathematics

Problem

Which of the following conditions guarantees that a real function ff is continuous at x=cx=c? a) lim⁡x→c−f(x)=lim⁡x→c+f(x)\displaystyle \lim_{x\to c^-} f(x)=\lim_{x\to c^+} f(x) b) lim⁡x→c−f(x)=lim⁡x→c+f(x)=f(c)\displaystyle \lim_{x\to c^-} f(x)=\lim_{x\to c^+} f(x)=f(c) c) lim⁡x→cf(x) exists\displaystyle \lim_{x\to c} f(x)\text{ exists} d) lim⁡x→c−f(x)=f(c)\displaystyle \lim_{x\to c^-} f(x)=f(c)

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