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 the eight examples this site. Attempt to match up problems in the homework with these examples. While the exact problems will vary, the algebra skills needed for many of the limits we will encounter will be related to these 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 sections 2.2 and 2.3, keeping the examples mentioned above in mind. Once you begin to easily spot the type of algebra that will be needed, work out the following three limits (by hand):
Then send an email to your instructor with the following three lines (with the blanks filled in, of course): Problem
number 1 is similar to example ___, and the limit is ____. To keep the email simple, you do not need to send the details of your solutions, only the three sentences requested above. 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. If your email program is configured properly, you can click on the name of your instructor (below) to send the email. Use the subject line `Your Name, Math 207 Limit Activity'. |
