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Unformatted text preview: MATH 20C — MIDTERM #2 REVIEW SHEET The second midterm will be during lecture slot on Friday, February 18th. It will be cumulative, but will focus on the material we have covered from chapter 14 since the first midterm (sections 14.1 through 14.7, not 14.8). As was the case for the first midterm, you may bring with you one letter-size sheet of paper which may be written on both sides. No other aids or references (including calculators) will be allowed. The following problems are intended to be similar to the problems that will be on the midterm. They are only to help you review and need not be turned in or graded; solutions will be posted next week. I also suggest that you go over the assigned homework problems, and if there are some you had trouble with, do some more similar exercises from the book. Note that there are also review questions at the end of each chapter of the book. 1. Sketch the contour map of f ( x,y ) = 3 x + 2 y with contour interval m = 2. 2. What do the vertical traces of the graph of the function f ( x,y ) = sin( x/y ) look like? 3. Sketch the contour maps of f ( x,y ) = sin( x 2 + y 2 ) with contour intervals m = 1 and 1 2 . 4. True or false? (a) If the partial derivatives f x and f y both exist at a point ( x,y ) = ( a,b ), then the function f is differentiable at ( a,b ). (b) If lim ( x,y ) → (0 , 0) f ( x,y ) exists, and the one-variable limit lim x → f ( x, 0) = 4, then lim ( x,y ) → (0 , 0) f ( x,y ) = 4....
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- Fall '07
- Derivative, differentiable function