A function is such that as approaches from the left

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

Problem

A function

h

is such that as

x

approaches

1

from the left,

h(x)

approaches

4

, and as

x

approaches

1

from the right,

h(x)

approaches

2

. No point is plotted at

x=1

. Which statement is most accurate concerning

\displaystyle \lim_{x\to 1} h(x)

? (a) The limit equals

4

because the left-hand values approach

4

. (b) The limit does not exist because the one-sided limits are not equal. (c) The limit equals

3

because it is the average of the one-sided limits. (d) The limit does not exist because

h(1)

is not defined.