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Computing Limits - Practice Problems Solutions

Computing Limits - Practice Problems Solutions - Calculus I...

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Calculus I © 2007 Paul Dawkins 1 http://tutorial.math.lamar.edu/terms.aspx Preface Here are the solutions to the practice problems for my Calculus I notes. Some solutions will have more or less detail than other solutions. The level of detail in each solution will depend up on several issues. If the section is a review section, this mostly applies to problems in the first chapter, there will probably not be as much detail to the solutions given that the problems really should be review. As the difficulty level of the problems increases less detail will go into the basics of the solution under the assumption that if you’ve reached the level of working the harder problems then you will probably already understand the basics fairly well and won’t need all the explanation. This document was written with presentation on the web in mind. On the web most solutions are broken down into steps and many of the steps have hints. Each hint on the web is given as a popup however in this document they are listed prior to each step. Also, on the web each step can be viewed individually by clicking on links while in this document they are all showing. Also, there are liable to be some formatting parts in this document intended for help in generating the web pages that haven’t been removed here. These issues may make the solutions a little difficult to follow at times, but they should still be readable. Computing Limits 1. Evaluate ( ) 2 2 lim 8 3 12 x x x fi - + , if it exists. Solution There is not really a lot to this problem. Simply recall the basic ideas for computing limits that we looked at in this section. We know that the first thing that we should try to do is simply plug in the value and see if we can compute the limit. ( ) ( ) ( ) 2 2 lim 8 3 12 8 3 2 12 4 50 x x x fi - + = - + = 2. Evaluate 2 3 6 4 lim 1 t t t fi- + + , if it exists. Solution There is not really a lot to this problem. Simply recall the basic ideas for computing limits that we looked at in this section. We know that the first thing that we should try to do is simply plug in the value and see if we can compute the limit.

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Calculus I © 2007 Paul Dawkins 2 http://tutorial.math.lamar.edu/terms.aspx 2 3 6 4 6 3 lim 1 10 5 t t t fi- + - = = - + 3. Evaluate 2 2 5 25 lim 2 15 x x x x fi- - + - , if it exists. Solution There is not really a lot to this problem. Simply recall the basic ideas for computing limits that we looked at in this section. In this case we see that if we plug in the value we get 0/0. Recall that this DOES NOT mean that the limit doesn’t exist. We’ll need to do some more work before we make that conclusion. All we need to do here is some simplification and then we’ll reach a point where we can plug in the value. ( )( ) ( )( ) 2 2 5 5 5 5 5 25 5 5 lim lim lim 2 15 3 5 3 4 x x x x x x x x x x x x fi- fi- fi- - + - - = = = + - - + - 4. Evaluate 2 8 2 17 8 lim 8 z z z z fi - + - , if it exists.
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