Prove function is continuous, multivariable

  • #1

Main Question or Discussion Point

Problem: If c is in Vn, show that the function f given by f(x) = c.x (c dot x, where both c and x are vectors) is continuous on ℝn.

How do I go about proving this? I'm not sure if c is supposed to be a constant or a constant vector, but since it is bolded in the book I am assuming it is a vector. Also, I'm not sure what Vn is. Finally, how do I show it is continuous?

As you can probably see, I am very lost. Any help would be appreciated.
 

Answers and Replies

  • #2
arildno
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"I'm not sure what Vn is."
--
Nor am I.
However, your book has most probably defined it, say as an n-dimensional vector space with a norm function associated with it.

So, your first exercise is to scrutinize your book for the DEFINITIONS of the terms used in the actual exercise.
 

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