# Introduction to Limits

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Introduction to Limits
5.2.1 Introduction to Limits

Limits Today you will follow the travels of Benny and Bertha Bug. With their help, we will look at graphs of rational functions and piecewise functions from a bug’s eye view to help convey the important concept of limits in an intuitive way.

5-41. Sketch the graph of f(x) = + 3.
Place a bold dot on the point of the graph corresponding to x = 5. Benny Bug starts at this location and crawls along the curve, moving to the right. If he keeps going in this direction, what y-value does Benny think he’s getting closer to? _____ As Benny keeps going farther and farther to the right, how low does Benny think he will get? _____

5-42. Consider the graph below when answering the questions below.

5-43 Look at your graph of f(x) = + 3
As x gets larger and larger, f(x) gets closer and closer to 3.

MATH NOTES - Definition of a One-Sided Limit
The formal definition of a limit is well beyond this course. If you take engineering or calculus, you will get it there. For now you need to understand the basic notation. We say x → c+ if the values of x get closer and closer to c from the right; that is, x > c. Similarly, x → c− if the values of x get closer and closer to c from the left.

MATH NOTES - Definition of a One-Sided Limit
If f(x) gets closer and closer to a given number L as x → c+, we say, “The limit of f(x) as x goes to c from the right is L.” This is written as If f(x) grows without bound we say If f(x) gets closer and closer to a number M as x → c−, we write

MATH NOTES - Definition of a One-Sided Limit
You should know that although most college textbooks give ∞ as a limit (as shorthand for f(x) growing without bound), some books say “no limit.”