Bilinear Function: |B(h,k)| / |(h,k)| = 0 for Lim (h,k) -> (0,0)

[brydustin]

{ lim (h,k) -> (0,0) } |B(h,k)| / |(h,k)| = 0 for an arbitrary bilinear function. But why? It seems obvious if B = 0 but this is true for ANY bilinear. I'm trying to figure this out so that I can see the definition a general derivative better.

 

[HallsofIvy]

What does |(h,k)| mean?

 

[brydustin]

Presumably, |(h,k)| is the norm of the bilinear argument... which without a bilinear acting upon it is perhaps the norm of the inner product (dot product)?