Unit 1B

Limits

Lesson 1: Introduction to Limits of Functions

In 2013, the world population surpassed 7 billion individuals, and it continues to rapidly increase, especially in developing countries. At some point in the future, the number of people inhabiting the Earth will reach a maximum, called the carrying capacity. There will no longer be enough space, water, food, and other resources to support any more people. In mathematical terminology, the population is approaching a limit. This means the world’s population is getting closer and closer to its carrying capacity as the year gets closer and closer to a certain value.

A limit of a function is the value of the function as the input approaches a certain value. This is expressed as follows.


This definition means as the values of «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»x«/mi»«/mstyle»«/math» get closer and closer to «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»a«/mi»«/mstyle»«/math», the values of «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«/mstyle»«/math» get closer and closer to «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»L«/mi»«/mstyle»«/math».