20cpracmidterm2 - Math 20C Practice Midterm 2 Lin Place all...

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Unformatted text preview: Math 20C Practice Midterm 2 Lin Place all books and papers under your desk. You may have one side on an 8-1/2 11 sheet of hand- written notes. On the cover of your blue book write your name, student ID number, section time, and color of your exam. In a column number one to four. Show all your work and give reasons for your answers. Box your answers. 1. (a) 5 pts. Let f ( x, y, z ) = x 3 + yz- xz . Find the directional derivative of f at (1 ,- 1 , 4) in the direction of <- 1 , 2 , 2 > . (b) 5 pts. A bugs elevation is given by z = x 2 + xy + 2 y 2 . When the bug reaches the point (2 , 1 , 8) he wants to head in a different direction where he avoids any vertical change. (He wants the directional derivative to be zero). In which direction should he head? (c) 5 pts. Find the equation of the tangent plane to the surface 4 x 2- y 2 + 3 z 2 = 10 at (2 ,- 3 , 1). (d) 10 pts. In what direction does the directional derivative for f ( x, y ) = x 2 y at (1 , 1) have value 1?...
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