MATH 3220	SECOND HOMEWORK ASSIGNMENT	Sept. 5, 2000
A. Treibergs		Due Sept. 12, 2000

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• Please write up the following exercises from the text "Introduction to Analysis, Second Edition" by William Wade, Prentice Hall 1999.
  • 244[1c,2b,6], 251[2,8].
• Here are the equivalent exercises for those using the First Edition:
  • 251[2c,1d,4],
  • Let  f(x,y)=(xy, x+y,x²-y²).  Using Definition 6.4 prove that  f  is differentiable on  R²  and its total derivative is given by

    Df(x,y) = [

    y   x 1   1 2x   -2y

    ]

  • Let  X  and  Y  be Euclidean Spaces. Show that if  T ∈ £(X,Y)  is linear then  T  is differentiable everywhere on  X  with
    DT(a) = T    for all    a ∈ X.