Introduction to Limits
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Provide an in-depth introduction to help students understand the concept of a limit.
Provide three detailed examples of finding limits.
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Solution Summary
In this solution, an introduction is given to develop an intuitive understanding of limits. Limit notation is introduced and examples are given of a case where the function exists at the limit, a case where the function does not exist and the limit does not exist, and a case where the function does not exist but the limit does exist.
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Imagine a tiny microscopic mouse, so tiny that it occupies no space. The mouse is one foot from a cookie. It can cover half its distance to the cookie in one move. So, in its first move, it covers 1/2 foot. In its second move, it covers
a distance of 1/4 foot so that at the end of its second move it is 1/4 foot from the cookie. At the ...
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