Math213H-F11-midterm2-v2

Math213H-F11-midterm2-v2 - Math213H01 EXAMII October26,2011...

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Math 213 H01 EXAM II October 26, 2011 Read each problem carefully. Show all work for each problem. No electronic devices or notes allowed 1. (16 pts) Find the limit, or show that it does not exist: a. 23 44 (,) ( 0 , 0 ) lim xy x y x y b. 33 0 , 0 ) lim x y x y c. 2 0 , 0 ) sin( ) lim x y x 2. (18 pts) For the function 2 (, ) 1 2 f xy x y  a. Find the domain and the range of this function b. Sketch several level curves of this function, indicating the function value for each c. Find the linearization of the function at point (1,1), and use it to estimate f (1.2, 0.9) d. Use the quadratic approximation to find a better estimate for f (1.2, 0.9) 3. (18 pts) Consider the surface 32 (, ,) 5 3 1 z Fxyz x y x y e z  a. Find the plane tangent to this surface at point (1, 1, 0)
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