Presentation on theme: "Introduction to Limits"— Presentation transcript:
1 Introduction to Limits 5.2.1Introduction to Limits
2 LimitsToday 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.
3 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? _____
4 5-42. Consider the graph below when answering the questions below.
5 5-43 Look at your graph of f(x) = + 3 As x gets larger and larger, f(x) gets closer and closer to 3.
6 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.
7 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 asIf f(x) grows without bound we sayIf f(x) gets closer and closer to a number M as x → c−, we write
8 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.”