Homework & Practice
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Math 241, Section 11 and 12
Fall 2014
Lecture: Tuesday, Thursday 1:302:45, in Keller 303
Instructor:
Ralph Freese
Office: 305 Keller Hall
email:email me
Office hours:
TuTh 2:453:15
and by appointment
TA:
Korey Nishimoto
Office: 412 Keller Hall
email:email him
Office hours: tba
Welcome to Math 241
Final Dec 17, noon to 2, Keller 303
What to study:

Practice and Extra Credit.
Practice final.
Turn this in on the day of final
for some extra credit.
We will go over this in the special help session.
Here are some
hints and solutions.

Do the problems on Professor Dovermann's
practice test.

Do the suggested problems from
Homework and Practice.

Memorize the three definitions at the bottom of this page.

Makeup and Practice Test for the midterms: Download and print the
the test file.
Directions are on the test. It is due Nov 6 in class.
Leibnitz's Rule
\[
\frac{d}{dx} \int_{r(x)}^{s(x)} f(t)\,dt = f(s(x))\,s'(x)  f(r(x))\,r'(x)
\]
Volumes
Volume of an Object with Cross Sectional Area \(A(x)\):
\[
V = \int_a^b A(x)\,dx
\]
Volume of Rotation of \(f(x)\) around the \(x\)axis:
\[
V = \pi\int_a^b f(x)^2\,dx
\]
Volume of Rotation of the region between \(f(x)\) and \(g(x)\),
\(f(x) \ge g(x) \ge 0\) around the \(x\)axis:
\[
V = \pi\int_a^b (f(x)^2  g(x)^2)\,dx
\]
Definitions to Memorize
Definition of Limit:
\(\lim_{x \to a} f(x) = L\) means
that for all \(\epsilon \gt 0\)
there is a \(\delta \gt 0\) such that
\(f(x)  L \lt \epsilon\) whenever \(0 \lt x  a \lt \delta\).
Continuity:
\(f\) is continuous at \(a\) if \(\lim_{x \to a} f(x) = f(a)\).
Derivative:
\[f'(x) = \lim_{h \to 0} \frac{f(x+h)  f(x)}{h}\].
