Becoming proficient at calculating limits requires a fairly solid understanding of what it is that a limit is measuring. In class we discussed the notion of a limit. This discussion lead to a realization that terms like "near" and "small" can be difficult to fully understand. The problems discussed in the activities below will help us perform calculations, but to better understand what it is we are calculating, view the first four lessons at this web site. You will need a computer that can play (flash) animations and sound (and the lessons may take a few moments to load). Limits are the foundation upon which calculus is built, so the time spent attempting to understand limits will likely pay off all semester.
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In order to be consistently successful when computing limits, you need strong algebra skills. Algebra is a large branch of mathematics, and while skills from nearly every part of algebra can come up from time to time in calculus, certain algebra skills are needed more often. To ensure that your knowledge of algebra contains these skills, read over examples 1,2,3,4 and 6 at the this site. Attempt to match up problems in the homework with these examples. While the exact problems will vary, the algebra skills needed for most of the limits we will encounter will be related to these few examples.
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In this activity, you will send an email to your instructor with the answer to a few limit problems. The goal of this activity is to learn to spot the sort of algebra steps that are included in the examples above. Work out the problems in section 3.1 in your text book and look over additional problems contained in the "Guided Problems" link. Keep the above examples in mind while you work through the problem sets, and when you see a match between the algebra skills needed for one of your problems and one of the examples, make a note. Once you begin to easily spot the type of algebra that will be needed, work out the following three limits (by hand):
When you submit the quiz survey (below), you should be prepared to answer the following: Problem
number 1 is similar to example ___, and the limit is ____. When listing the answers to the limits, write the number if the limit is a finite value. Use the words 'positive infinity' if the limit goes to positive infinity, use the words 'negative infinity' if that is the limit. If the limit does not exist and is not either infinity or negative infinity, write DNE. Final Step: Once you have completed the activities above and have learned about limits, click on the Survey below and answer the questions (your responses will be sent to your instructor): Use our email login and password to get into the survey.
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