# Question: Let f Rn R be a function such that f x x

Let f: Rn →R be a function such that | f (x) | ≤ |x|2 . Show that f is differentiable at 0

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Let f: R→R 2. Prove that f is differentiable at a € R if and only if f 1 and f 2 are, and in this case f 1(a) = ((f 1)1 (a) (f 2)1 (a)).Define IP: Rn x Rn →R by IP (x, y) = . (a) Find D(IP) (a,b) and (IP)’ (a,b). (b) If f,g: R → Rn are differentiable, and h: R → R is defined by h(t) = , show that hI (a) = Define f: R → R by f (x) = { e-x-2 x ≠ 0,. 0 x -0,} a. Show that f is a C00 function, and f(i) (0) = 0for all .Let f be defined as in Problem 2-4. Show that Dxf (0, 0) exists for all , but if g ≠ 0, , then Dx + yf (0,0) =Dxf (00 Dx + y f (0, 0) = Dx f (0 , 0) + Dyf (0, 0) Is not true for all x and all y.a. If f : R → R satisfies f1 (a) ≠ 0 for all a €R, show that f is 1-1 on all of R.Post your question