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tutorial3 - f at the point a =(1 0 in the direction of u =...

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MATH1211/10-11(2)/Tu3/TNK THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH1211 Multivariable Calculus 2010-11 2nd Semester: Tutorial 3 Date of tutorial classes: February 17–18. (The section/problem numbers in the following refer to those in the textbook.) 1. ( § 2.5 no.4) Suppose that z = x 2 + y 3 , where x = st and y is a function of s and t . Suppose further that when ( s,t ) = (2 , 1), ∂y/∂t = 0. Determine ∂z ∂t (2 , 1). 2. ( § 2.5 no.12) If w = f ± x 2 - y 2 x 2 + y 2 ² is a differentiable function of u = x 2 - y 2 x 2 + y 2 , show that then x ∂w ∂x + y ∂w ∂y = 0 . 3. Let f ( x,y ) = xe 2 y + x 3 . (a) Calculate the directional derivative of the
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Unformatted text preview: 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? 4. ( § 2.6 no.18) 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 ,y ,z ) = (1 ,-5 , 5). 5. ( § 3.1 no.18) Find an equation for the line tangent to the path x ( t ) = (cos( e t ) , 3-t 2 , t ) at t = 1. 1...
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