# A3f - 1 in the direction of the vector v =(3 4 b Is there a...

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Math 237 Assignment 3 Due: Friday, Oct 10th 1. Determine all points where the function is diﬀerentiable. a) f ( x, y ) = x 1 / 3 b) g ( x, y ) = ± x 2 y 2 x 2 + y 2 if ( x, y ) 6 = (0 , 0) 0 if ( x, y ) = (0 , 0) . c) h ( x, y ) = ± x 2 / 3 y 4 / 3 x 2 + y 2 if ( x, y ) 6 = (0 , 0) 0 if ( x, y ) = (0 , 0) . 2. Write the chain rule for ( ∂w ∂x ) y if w = F ( u, v, x, y ), and u = u ( x ), v = v ( x, y ), where x and y are independent variables. 3. Let f ( s, t ) = e x sin( x 2 + y 2 ) where x = x ( s, t ) = tan - 1 st and y = y ( t ) = t 3 . Find f s and f t . 4. Dorthy’s position at any time t is given by ( x, y, z ) = ( t cos t, t sin t, 2 t ). The air temperature at any point ( x, y, z ) is given by a function T : R 3 R . If T ( - π, 0 , 2 π ) = (1 , - 2 , 1) then determine the rate of change of temperature Dorthy experiences at time t = π . 5. Let f ( x, y ) = x 2 e y 2 . a) Find the directional derivative of f at (2 , -
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Unformatted text preview: 1) in the direction of the vector v = (3 , 4). b) Is there a direction at (2 ,-1) in which the rate of change of f is equal to 18? Justify your answer. c) Find the direction at (2 ,-1) in which the rate of change of f is the greatest. 6. Let f ( x, y ) = ± x 2 y x 4 + y 2 if ( x, y ) 6 = (0 , 0) if ( x, y ) = (0 , 0) . a) Find the directional derivative D (1 , 2) f (0 , 0). b) Deduce that f is not diﬀerentiable at (0 , 0). 7. Find the equation of the tangent plane to the surface 3 = x 2 + 2 y 2-3 z 2 at the point (2 , 1 , 1)....
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## This note was uploaded on 04/18/2010 for the course MATH 237 taught by Professor Wolczuk during the Spring '08 term at Waterloo.

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