2.3: Limits
In this subunit, you will take a close look at a concept that you have used intuitively for several years: the limit. The limit asks the question, "what does the function do as the independent variable becomes closer and closer to a certain value?" In simpler terms, the limit is the natural tendency of a function. The limit is incredibly important due to its relationship to the derivative, the integral, and countless other key mathematical concepts. A strong understanding of the limit is essential to success in the field of mathematics.
2.3.1: The Definition and Properties of Limits
Read Section 2.3 (pages 36-45). Read this section carefully, and pay close attention to the definition of the limit and the examples that follow. You should also closely examine the algebraic properties of limits as you will need to take advantage of these in the exercises.
Watch this video.
Work through problems 1-18 for Exercise 2.3. When you are done, check your answers against Appendix A.
Work through problems 1-10. When you are done, check your solutions against the answers provided.
2.3.2: The Squeeze Theorem
Read section 4.3 (pages 75-77). The Squeeze Theorem is an important application of the limit concept and is useful in many limit computations. This reading teaches you a useful trick for calculating limits of functions where at first glance you might seem to be dividing by zero.
Watch this brief video. The creator of this video describes and illustrates the Squeeze Theorem by using specific examples.