(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let f: R^n X R^m --> R^p be a bilinear function.

Prove that |f(h, k)|/|(h, k)| --> 0 as (h, k) --> 0 (zero vector in R^(n+m)).

2. Relevant equations

If f: R^n X R^m --> R^p is bilinear, then for x, x1, x2 in R^n, y, y1, y2 in R^m, a in R:

a) f(ax, y) = f(x,ay) = af(x,y)

b) f(x1+x2,y) = f(x1,y) + f(x2,y)

c) f(x,y1+y2) = f(x,y1) + f(x,y2)

3. The attempt at a solution

Straight from delta-epsilon definition of limit, we have:

for every epsilon>0, there exist delta>0 s.t. |(h,k)|<delta -> |f(h,k)|/|(h,k)|<epsilon

That means delta>|f(h,k)|/epsilon

I'm stuck on this. How do I find a bound on |f(h,k)| using the bilinear properties given?

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# Homework Help: Bilinear functions

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