Math 317 HW #11
Due 5:00 PM Thursday, December 2
Reading:
Abbott §5.3–5.4.
Problems:
1. Exercise 5.3.1.
2. Exercise 5.3.6.
3. Exercise 5.3.8. A more precise statement of the last part would be: “Say why the function in
Exercise 5.3.7(b) is not a counter-example to the statement you just proved”.
4. Exercise 5.3.13. The statement of the question is slightly misleading. What you should do is
prove the following version of L’Hôpital’s Rule:
Theorem 4.1. Assume f and g are differentiable on an interval containing a, except possibly
at a itself. If limx→a f (x) = 0 and limx→a g(x) = 0, then
f 0 (x)
=L
x→a g 0 (x)
lim
implies
5. Exercise 5.4.6.
1
f (x)
= L.
x→a g(x)
lim