Section 4.4 Worksheet: Limits at Infinity, Asymptotes

Assigned problems: Exercises pp. 260-263, #2, 3, 10, 16, 38, 42, 56 (due Friday, 3/7).

1. What do we mean by ``end behavior'', and how does a horizontal asymptote fit into that scheme?
2. What is the relationship between vertical asymptotes and horizontal asymptotes?
3. Suppose that f is differentiable as , and f has a horizontal asymptote of y=3. What can we say about the derivative function as ?
4. What kinds of end behavior are possible for rational functions? For polynomials (of degree > 0)?

Notes:

1. Don't worry too much about the ``precise definitions''. You might want to look that over, anyway, of course!

2. We're interested in the behavior of the function at its extremes, far from 0. This is very common in many areas of business or science: in astronomy, for example, when we're looking at the effects of Earth's gravity on a spaceship near the sun (it's essentially negligable - i.e., Earth's gravity(great distance) is about 0: ).