Unformatted text preview: The Limit of a Function Consider the function Domain ? What happens to the function near ? Both the numerator and denominator gets closer and closer to What happens to the graph near ? It exists, seems to be near As the values of become ever closer to , what is happening to the corresponding -values ? get ever closer to , This graph has a "hole" in it at Definition: We write lim and say "the limit of , as approaches , equals ." by taking to be if we can make the values of arbitrarily close to sufficiently close to , but not equal to . MTH 173, section 2.2, page 1 102-6 lim undefined, lim lim detail near does not exist. lim detail below MTH 173, section 2.2, page 2 Now let's consider Domain? What happens to the graph near Let's look at the graph and ? Does the lim exist? 14. Sketch the graph of a function that satisfies the following: lim lim undefined lim lim MTH 173, section 2.2, page 3 16. Estimate the limit by evaluating at the given -values lim We can use a spreadsheet to calculate: appears to not tend to one number, so probably the limit does not exist. 20. estimate lim tan tan with a table 24. Determine the infinite limit lim MTH 173, section 2.2, page 4 34. Estimate lim MTH 173, section 2.2, page 5 ...
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- Fall '09
- lim, lim lim, lim undefined lim