Math 242, Fall 2013, Assignment 4

No doubt many people feel that the inclusion of mathematics among the arts is unwarranted. The strongest objection is that mathematics has no emotional import. Of course this argument discounts the feelings of dislike and revulsion that mathematics induces....

- Morris Kline, Mathematics in Western Culture

Carefully define the following terms:

1. Limit (of a vector function).
2. Derivative (of a vector function).
3. Definite integral (of a vector function).
4. Arc length (of a space curve).
5. Curvature (of a space curve).
6. Tangent, normal, and binormal vectors.
7. Normal plane.
8. Osculating plane.
9. Osculating circle.

Carefully state the following theorems:

1. Differentiation rules (Theorem 3 on page 704).
2. Curvature formula (Theorem 10 on page 710).

Solve the following problems:

1. Section 10.1, problems 1, 3, 7, and 9.
2. Section 10.2, problems 3, 15, 33, 37, and 49.
3. Section 10.3, problems 1, 13, 17, 23, and 47.

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