Near , the graph of a function oscillates rapidly between and without settling toward…

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

Problem

Near

x=0

, the graph of a function

h

oscillates rapidly between

y=1

and

y=-1

without settling toward any single value. Does

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

exist? State your conclusion and indicate the reason (unbounded behavior, oscillation, or unequal one-sided limits).