Mathematics

Problem

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

x=c

is a vertical asymptote of the graph of a function

f

? a)

\displaystyle \lim_{x\to c^-} f(x)\neq \lim_{x\to c^+} f(x)

, both limits finite b) At least one of

\displaystyle \lim_{x\to c^-} f(x)

\displaystyle \lim_{x\to c^+} f(x)

equals

\pm\infty

\displaystyle \lim_{x\to c} f(x)=0

\displaystyle \lim_{x\to c} f'(x)=\pm\infty