Homework & Practice

WeBWorK instructions

Syllabus

Lab

# Fall 2014

Lecture: Tuesday, Thursday 1:30-2:45, in Keller 303
Instructor: Ralph Freese
Office: 305 Keller Hall
email:email me
Office hours: Tu-Th 2:45-3:15 and by appointment
TA: Korey Nishimoto
Office: 412 Keller Hall
email:email him
Office hours: tba

## 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.

• 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: $f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$.