EXAM 2MATH 22Name: ____________________________Winter 2001Section: __________You must show all work clearlyto receive full credit. (8) 1)Find and sketch the domain of the function.fx yxyxy( ,)ln()=++--112222(10) 2) Determine the largest set on which the function g is continuous. Give your reasoning.g x yxyxxyy( , )=++220ifif( ,)( , )( ,)( , )x yx y≠=0 00 0(6) 3) Find if .¶¶zxxyzxyz=++ln()(8) 4) Determine if there exists a function f with and fx yxyx( , )cos()=+and whose second partial derivatives are continuous. Give yourfx yxyy( ,)sin()=--p2reasoning.(10) 5) Is differentiable at (2,2)? If not, give your reasoning. If so, find the fx yxy( ,)=linearization L(x,y) of f at (2,2).(8) 6) For , show that .fx yxyy( ,)=+22xfxyfyfx y¶¶¶¶+=2( ,)7) Given the surface , xzy222+=(8) (a) find the equation of the tangent plane to the surface at the point
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