2300hw2SP11 - t . (d) Find the unit tangent and normal...

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——————————————————————————————————– MATH 2300 - Calculus III Spring 2011 Homework 2 - DUE Wednesday, February 16 ——————————————————————————————————– 1. Let r ( t ) = e t sin t i + e t j + e t cos t k represent the path of a particle at time t . (a) If the particle starts at time t = 0, and moves a distance of 27 units along the path, when did the particle stop? (b) Find parametric equations of the tangent line to r ( t ) at t = π . (c) Determine whether the curve is smooth on 0
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Unformatted text preview: t . (d) Find the unit tangent and normal vectors ( T and N ) to the path at time t = 0. (e) Find the curvature of r ( t ) at the point (0 , 1 , 1). 2. Find the tangential and normal components of the acceleration of r ( t ) = e-t i + 2 t j + e t k at t = 0. 3. Find all constants a and b such that u ( x, y ) = cos( ax ) e by satises Laplaces equation: u xx + u yy = 0. 4. Given f ( x, y ) = y p 1 x + cos( xy ) P , nd 2 f yx and 2 f y 2...
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