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Math 241, Section 11 and 12

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

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

\[ \frac{d}{dx} \int_{r(x)}^{s(x)} f(t)\,dt = f(s(x))\,s'(x) - f(r(x))\,r'(x) \]


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