SECOND HOMEWORK ASSIGNMENT
Sept. 5, 2000
Due Sept. 12, 2000
Please write up the following exercises from the text "Introduction to Analysis, Second Edition" by William Wade, Prentice Hall 1999.
Here are the equivalent exercises for those using the First Edition:
Let f(x,y)=(xy, x+y,x
). Using Definition 6.4 prove that f is differentiable on
and its total derivative is given by
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.