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Prove function is continuous, multivariable

  1. Oct 27, 2013 #1
    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.
  2. jcsd
  3. Oct 27, 2013 #2


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    Dearly Missed

    "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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