Lecture 11: Finding Limits of SequencesMATH 137 Physics-based Section, Fall Term 2019Friday, September 27thReferences for additional readingCN: 1.2, 1.3, 1.4Stewart: 11.111.1Common techniques for limits of sequencesWe have been talking about sequences and their limits.It is not always easy to prove a limitusing theε–δdefinition.There are some “tricks” we can use for finding limits.In Section 10.3of the Lecture Notes, we stated some properties of limits, such as the arithmetic rules and theSqueeze Theorem. Before we introduce new results, let’s use these properties to determine somelimits.Question 1 of Problem Set 4 is very similar but concerns limits of functions rather thansequences.1. We can easily show thatlimn→∞1 = 1 using the definition of limits.2. We can also verify thatlimn→∞nα=(∞ifα >0,0,ifα <0.Some common examples arelimn→∞1/n2= limn→∞1/n= 0,limn→∞√n= limn→∞n=∞.
6. How can we evaluatelimn→∞