Practice Exam 2a - 110.107 Calculus II Fall 2012 Exam 2...

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110.107 Calculus IIFall 2012Exam 2 PracticeProblem 1Show that following limits does not exist.(a)lim(x,y)(0,0)x+yx2+y(b)lim(x,y)(0,0)x2+xyx2+y2Solution:
Problem 3LetG(x, x) =x2+xy2-y22andp= (-1,1)R2.(a) Calculate the equation of the plane tangent to the graph ofGat the pointp.(b) Calculate the gradient ofGat the pointp(that is, computeG(-1,1)).(c) Find a critical point ofG(x, y)on the domainR2and de-termine whether it is a local maximum, local minimum, orneither (Hint: The Hessian will help here.)

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