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Definition of a Derivative/Limit

  1. Oct 13, 2008 #1
    I'm in a multi-variable calculus course, and we need to know definitions for the test.

    Is this a correct definition of a derivative:

    Let [tex]f:R^n \rightarrow R^p[/tex] f is diffrentiable at x iff there exists a matrix (p x n) Df(x) such that [tex]lim (h\rightarrow0)\frac{f(x - h) -f(x) -Df(x)h}{||h||} = 0[/tex]

    My professor gave us quite a few definitions for derivative, some involve gradients and epsilon. Just wondering if the above also works.

    and is this a correct definition of a limit:

    [tex]lim (x \rightarrow x_0) F(x) = A [/tex] there exists [tex]\epsilon > 0[/tex] such that [tex]\delta>0 \Rightarrow [/tex] [tex]0<||x - x_0|| <\delta \Rightarrow ||f(x) - A|| < \epsilon[/tex]
  2. jcsd
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