The function is defined for all

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

Problem

The function

g

is defined for all

x\neq 2

. The table gives values of

g(x)

for

x

close to

2

. x g(x) 1.9 4.02 1.99 4.001 1.999 4.0001 2.001 4.9998 2.01 4.99 2.1 4.90 Which statement best describes the two–sided limit of

g

x

approaches

2

? (a) The limit exists and equals

4.5

, the average of the one–sided limits. (b) The limit does not exist because values approaching

2

from the left tend toward

4

while values from the right tend toward

5

. (c) The limit exists and equals

4

because values sufficiently close to

2

are near

4

. (d) The limit does not exist because

g(2)

is not provided in the table.