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Unformatted text preview: MATH 23 Sample Final Exam April, 2003 NAME : Section (Last, First) 1. (15 points ) (a) Find a vector perpendicular to the plane through (0 , 2 , 0) , (2 , 3 , 1) and (1 , 2 , 4) . (b) give an equation for the plane in part (a). 2. (10 points ) Find an equation for the tangent line to the curve→ r ( t ) = ( t 2 3) i 2 tj + t 2 k at the point P (1 , 4 , 4) . 3. (20 points ) The position function for the motion of a particle is given by→ r ( t ) = ti + 2 tj + t 2 k = < t, 2 t, t 2 > . (a) Find the velocity and acceleration vectors. (b) Find the tangential component a T of acceleration. (c) Find the curvature when t = 0. 4. (10 points ) Let f ( x, y, z ) = x 2 y + xyz 3 . Find each of the following. (a) ∂f ∂x (b) ∂ 2 f ∂x 2 (c) ∂ 2 f ∂z∂x (1 , 2 , 3) 5. (15 points ) Let f be the function f ( x, y ) = x 2 3 y 2 . (a) Find the directional derivative of f at the point (2 , 3) in the direction of the vector a = < 4 , 3 > = 4 i + 3 j....
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This note was uploaded on 09/06/2010 for the course MATH 23 taught by Professor Yukich during the Spring '06 term at Lehigh University .
 Spring '06
 YUKICH
 Math, Calculus

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