For a function it is known that while

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

For a function

g

it is known that

\displaystyle \lim_{x\to 0^-}g(x)=2

while

\displaystyle \lim_{x\to 0^+}g(x)=\infty

. Explain why

\displaystyle \lim_{x\to 0}g(x)

does not exist and specify whether the failure is due to a jump discontinuity or an unbounded (infinite) discontinuity at

x=0