Math 213‐H01EXAM IIOctober 26, 2011Read each problem carefully. Show all work for each problem. No electronic devices or notes allowed1.(16 pts)Find the limit, or show that it does not exist:a.2344(,) (0,0)limxyx yxyb.330,0)limx yxyc.20,0)sin()limx yx2.(18 pts)For the function2(, )1 2f xyx ya.Find the domain and the range of this functionb.Sketch several level curves of this function, indicating the function value for eachc.Find the linearization of the function at point (1,1), and use it to estimatef(1.2, 0.9)d.Use the quadratic approximation to find a better estimate forf(1.2, 0.9)3.(18 pts)Consider the surface32(, ,) 531zFxyzxyxyeza.Find the plane tangent to this surface at point (1, 1, 0)
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