7. Prove that

(x, y) =f (0,0)

(x, y) = (0,0)

(x, y) =f (0,0)

(x, y) = (0,0)

(x, y) =f (0,0)

(x, y) = (0,0)

is continuous on R 2 , has first-order partial derivatives everywhere on R 2 , but 1 is not differentiable at (0,0). 00. This exercise is used several times in this chapter and the next.

Let T E .C(Rn; Rm). Prove that T is differentiable everywhere on Rn with DT

(a) = T