CK-12-Pre-Calculus Concepts

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

limx→ 3 f(x) =^12

f( 3 ) = 3
limx→∞f(x) =DNE

Vocabulary

The phrase“does not exist”or“DNE”is used with limits to imply that the limit does not approach a particular
numerical value. Sometimes this means that the limit continues to grow bigger or smaller to infinity. Sometimes it
means that the limit can’t decide between two disagreeing values. There are times when instead of indicating the
limit does not exist, you might choose to write the limit goes to infinity. This notation is technically not correct, but
it does provide more useful information than writing DNE and therefore can be acceptable.

Guided Practice

1. Identify everywhere where the limit does not exist and where the limit does exist in the following function.


2. Evaluate and explain how to find the limits asxapproaches 0 and 1 in the previous question.


3. Evaluate the limits of the following piecewise function at -2, 0 and 1.

f(x) =

















2 x<− 2

− 1 x=− 2

−x− 2 − 2 <x≤ 0

x^20 <x< 1

− 2 x= 1

x^21 <x

Answers:

1. The limit does not exist atx=− 3 ,− 1 , 2 ,+∞,−∞. At every other point (includingx=1), the limit does exist.


2. limx→ 0 f(x) = 2 ,limx→ 1 f(x) = 1