2220hw3 - Math 2220 Problem Set 3 Spring 2010 Section 2.6 :...

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Unformatted text preview: Math 2220 Problem Set 3 Spring 2010 Section 2.6 : 4. Calculate the directional derivative of the function f ( x, y ) = 1 / ( x 2 + y 2 ) in the direction of the vector u = i j = (1 , 1) at the point (3 , 2). 6. Calculate the directional derivative of the function f ( x, y, z ) = xyz in the direction of the vector u = 2 k i 5 = 1 5 ( 1 , , 2) at the point ( 1 , , 2). 10. For the function f ( x, y ) = xy radicalbig x 2 + y 2 if ( x, y ) negationslash = (0 , 0) if ( x, y ) = (0 , 0) (a) calculate f x (0 , 0) and f y (0 , 0) (b) use Definition 6.1 (the definition of a directional derivative) to determine for which unit vectors v = ( v, w ) = v i + w j the directional derivative D v f (0 , 0) exists. 14. It is raining and rainwater is running off an ellipsoidal dome with equation 4 x 2 + y 2 + 4 z 2 = 16, where z 0. Given that gravity will cause the raindrops to slide down the dome as rapidly as possible, describe the curves whose paths the raindrops must follow.dome as rapidly as possible, describe the curves whose paths the raindrops must follow....
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2220hw3 - Math 2220 Problem Set 3 Spring 2010 Section 2.6 :...

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