For a function

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

Problem

For a function

f

, the graph satisfies the following near

x=3

: •

f(x)

approaches

2

x\to 3^{-}

. •

f(x)

approaches

8

x\to 3^{+}

. • The point

(3,5)

is filled on the graph. State (i)

\displaystyle \lim_{x\to 3^{-}}f(x)

, (ii)

\displaystyle \lim_{x\to 3^{+}}f(x)

, and (iii) whether

\displaystyle \lim_{x\to 3}f(x)

exists.