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A function f”R n × R m → R is bilinear if for all x, y...

A function f”R n × R m → R is bilinear if for all x, y ∈ R n and all w, z ∈ R m, and all a ∈ R: • f(x + ay, z) = f(x, z) + af(y, z) • f(x, w + az) = f(x, w) + af(x, z) (a) Prove that if f is bilinear, then (0.1) lim (h,k)→(0,0) |f(h, k)| |(h, k)| = 0. (b) Prove that Df(a, b) · (h, k) = f(a, k) + f(h, y).

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