Which of the following conditions is sufficient to conclude that the line is a…

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

Problem

Which of the following conditions is sufficient to conclude that the line x=cx=c is a vertical asymptote of the graph of a function ff? (a) lim⁡x→c−f(x)≠lim⁡x→c+f(x)\displaystyle \lim_{x\to c^-} f(x)\neq \lim_{x\to c^+} f(x), both limits finite (b) At least one of lim⁡x→c−f(x)\displaystyle \lim_{x\to c^-} f(x) or lim⁡x→c+f(x)\displaystyle \lim_{x\to c^+} f(x) equals ±∞\pm\infty (c) lim⁡x→cf(x)=0\displaystyle \lim_{x\to c} f(x)=0 (d) lim⁡x→cf′(x)=±∞\displaystyle \lim_{x\to c} f'(x)=\pm\infty

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