14.6. One Sided Limits and Continuity http://www.ck12.org
Vocabulary
Aone sided limitis a limit of a function when the evidence from only the positive or only the negative side is used
to evaluate the limit.
Continuity for a pointexists when the left and right sided limits match the function evaluated at that point. For an
entire function to be continuous, the function must be continuous at every single point in an unbroken domain.
Guided Practice
- Megan argues that according to the definition of continuity, the following function is continuous. She says
- limx→ 2 −f(x) =∞
- limx→ 2 +f(x) =∞
- f( 2 ) =∞
Thus since limx→ 2 −f(x) =f( 2 ) =x→lim 2 +f(x), it meets the definition of continuous. How could you use the graph below
to clarify Megan’s reasoning?
- Evaluate the following limits.
a. limx→ 1 −( 2 x− 1 )
b.x→−lim 3 +(x+^22 )
c. limx→ 2 +(x (^3) − 8
x− 2
)
- Is the following function continuous?
f(x) =
x^2 − 1 x<− 1
3 x=− 1
−x+ 3 − 1 <xAnswers: