Tutorial 4

Tutorial 4 - x ( t ) = ( e t ,e 2 t , 2 e t ). 4. Find an...

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MATH1211/10-11(1))/Tu4 THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH1211 Multivariable Calculus 2010-11 First Semester: Tutorial 4 1. Let f ( x,y ) = xe 2 y + x 3 . (a) Calculate the directional derivative of the f at the point a = (1 , 0) in the direction of u = i - j . (b) At the point a = (1 , 0), in which direction will f increase fastest, and how fast is it? 2. Find an equation for the tangent plane to the surface given by the equation 2 xz + yz - x 2 y + 10 = 0 at the point ( x 0 ,y 0 ,z 0 ) = (1 , - 5 , 5). 3. Calculate the velocity, speed, and acceleration of the path
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Unformatted text preview: x ( t ) = ( e t ,e 2 t , 2 e t ). 4. Find an equation for the line tangent to the path x ( t ) = (cos( e t ) , 3-t 2 , t ) at t = 1. 5. Calculate the length of the path x ( t ) = t 2 i + 2 3 (2 t + 1) 3 / 2 j , 0 ≤ t ≤ 4. 6. Determine the moving frame [ T , N , B ], and compute the curvature and torsion for the path x ( t ) = (sin t-t cos t ) i + (cos t + t sin t ) j + 2 k , t ≥ 0. 1...
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