At , the graph of a function has an open circle at and a solid dot at . The curve…

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

Problem

x=2

, the graph of a function

g

has an open circle at

(2,5)

and a solid dot at

(2,3)

. The curve approaches the

y

-value

5

from both sides as

x

approaches

2

. Which of the following statements is true? (a)

\displaystyle \lim_{x\to 2}g(x)

exists and

g

is continuous at

x=2

(b)

\displaystyle \lim_{x\to 2}g(x)

does not exist but

g

is continuous at

x=2

(c)

\displaystyle \lim_{x\to 2}g(x)

exists but

g

is not continuous at

x=2

(d) Neither does

\displaystyle \lim_{x\to 2}g(x)

exist, nor is

g

continuous at

x=2