Question: Name: Worksheet 4 Math 32A 1. Let r(t) = (cos 1?, sint, cost). (a) Draw a big picture of the curve r(t], and describe its

Name: Worksheet 4 Math 32A 1. Let r(t) = (cos 1?, sint, cost). (a) Draw a big picture of the curve r(t], and describe its shape. Hint: break r(t) up into (1,0,1) and (0,1,0) components. (b) Compute the velocity and speed of r(t). Draw two velocity vectors onto the picture from the previous part. (c) Find an arc length parametrization of the space curve parametrized by r(t). (d) Find the curvature of r(t) using the following denition: dzr me) = ' e) Explain Why for our curve the curvature does not depend on s. (e) Use the formula W, : ||r'(t) >

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