prac2a - MIT OpenCourseWare http:/ocw.mit.edu 18.02...

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MIT OpenCourseWare http://ocw.mit.edu 18.02 Multivariable Calculus Fall 2007 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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18.02 Practice Exam 2 A Problem 1. (10 points: 5, 5) Let f ( x,y ) = xy x 4 . a) Find the gradient of f at P : (1 , 1). b) Give an approximate formula telling how small changes Δ x and Δ y produce a small change Δ w in the value of w = f ( x,y ) at the point ( x,y ) = (1 , 1). Problem 2. (20 points) On the topographical map below, the level curves for the height function h ( x,y ) are marked (in feet); adjacent level curves represent a difference of 100 feet in height. A scale is given. dh a) Estimate to the nearest .1 the value at the point P of the directional derivative , where ds u ˆ u ˆ is the unit vector in the direction of ˆ ı +ˆ . ∂h ∂h b) Mark on the map a point Q at which h = 2200, = 0 and < 0. Estimate to the nearest .1 ∂h ∂x ∂y the value of at Q . ∂y
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This note was uploaded on 05/04/2011 for the course MATH 18.02 taught by Professor Auroux during the Spring '08 term at MIT.

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prac2a - MIT OpenCourseWare http:/ocw.mit.edu 18.02...

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