CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 14. Concepts of Calculus

Evaluate the following expressions using the graph of the functionf(x).

a. limx→−∞f(x)

b. limx→− 1 f(x)

c. limx→ 0 f(x)

d. limx→ 1 f(x)

e. limx→ 3 f(x)

f. f(− 1 )

g. f( 2 )

h. f( 1 )

i. f( 3 )

Solution:

a. limx→−∞f(x) = 0

b. limx→− 1 f(x) =DNE

c. limx→ 0 f(x) =− 2

d. limx→ 1 f(x) = 0

e. limx→ 3 f(x) =DNE(This is because only one side exists and a regular limit requires both left and right sides

to agree)

f. f(− 1 ) = 0

g. f( 0 ) =− 2

h. f( 1 ) = 2

i. f( 3 ) = 0

Example B
Sketch a graph that has a limit atx=2, but that limit does not match the height of the function.
Solution:While there are an infinite number of graphs that fit this criteria, you should make sure your graph has a
removable discontinuity atx=2.