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317-w09-202-hw-02

# 317-w09-202-hw-02 - Math 317 Section 202 Homework no 2(due...

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Math 317, Section 202, Homework no. 2 (due Friday (!) January 22, 2010) [7 problems, 36 points] Problem 1 (6 points) . Suppose the curve C is the part of the intersection of the cylinder x 2 + y 2 = 1 with the plane x + y + z = 1 for which y 0. 1. (3 points) Parameterize C by a vector function r ( t ) such that the parameter t is (a) the polar angle in the xy -plane, (b) t = x , (c) t = - x . 2. (3 points) For each of the three parameterizations, compute the tangent vector to C , the unit tangent vector and a parameterization of the tangent line, all at the point ( 1 2 , 1 2 , 1 - 2). Problem 2 (4 points) . Just answer Yes or No (Y/N) to the following questions; no explana- tion required. Consider the curve C parameterized by r ( t ) = t 3 , 2 t 3 - 1 , - t 3 + 2 , -∞ < t < . (a) (1 point) Is the parameterization smooth? (b) (1 point) Is the curve smooth? Consider the curve ˜ C parameterized by ˜ r ( t ) = 1 - t 2 , 1 - t 2 , 0 t 1 2 . (c) (1 point) Is the parameterization smooth? (d) (1 point) Is the curve smooth?

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317-w09-202-hw-02 - Math 317 Section 202 Homework no 2(due...

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