# MATH_207_Spring_2011_Solution_3 - MATH 207 Spring 2011 Dr....

MATH_207_Spring_2011_Solution_3
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MATH 207 Spring 2011 Dr. Smith Assignment 3 Total possible is 50 1. Find the limit if it exists, or show that the limit does not exist. a) (14.2 #14) 2 2 4 4 ) 0 , 0 ( ) , ( lim y x y x y x + b) (14.2 #16) 2 2 2 2 ) 0 , 0 ( ) , ( 2 sin lim y x y x y x + Four points c) (14.2 # 20) 2 2 2 2 2 2 ) 0 , 0 , 0 ( ) , , ( 3 2 lim z y x z y x z y x + + + + Four points 2. Determine the set of points at which the function is continuous. a) (14.2 # 30) 2 2 1 ) , ( y x y x y x F + + = b) (14.2 #32) 2 2 ) , ( y x e y x f y x + + =
3. (14.2 # 40) Use polar coordinates to find . ) ln( ) ( lim 2 2 2 2 ) 0 , 0 ( ) , ( y x y x y x + + 4. Find all first partial derivatives for a) (14.3 #22) f(x,y) = x y Four points (2 for each partial) b) (14.3 #26) f(x,t) = arctan(x t) c) (14.3 #38) u = sin(x 1 + 2x 2 + … + nx n ) Four points 5. a) (14.3 #42). Find the partial derivative f z (0,0, π /4) if z y x z y x f 2 2 2 sin sin sin ) , , ( + + = Since f is a function of z, z is an independent variable. z
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