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

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The limit of the ratio |B(h,k)| / |(h,k)| approaches 0 as (h,k) approaches (0,0) for any arbitrary bilinear function B. This conclusion holds true regardless of whether B equals zero. The term |(h,k)| represents the norm of the bilinear argument, which can be interpreted as the norm of the inner product when no bilinear function is applied. Understanding this limit is crucial for grasping the definition of a general derivative in the context of bilinear functions.

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{ 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.
 
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What does |(h,k)| mean?
 
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)?
 

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