Near , the graph of a function behaves as follows: • As approaches from the left,…

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

Problem

Near

x=6

, the graph of a function

h

behaves as follows: • As

x

approaches

6

from the left,

h(x)

oscillates rapidly between

2

and

10

without settling at a single value. • As

x

approaches

6

from the right,

h(x)

approaches the finite value

5

. Which statement correctly describes

\displaystyle \lim_{x\to 6} h(x)

? (a) The limit exists and equals

5

. (b) The limit exists and equals

7

. (c) The limit does not exist because the left-hand limit fails to exist. (d) The limit does not exist because the left-hand limit equals

2

while the right-hand limit equals

5