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Math Help - Is the first principles?

  1. #1
    Junior Member piglet's Avatar
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    Is the first principles?

    Im trying to prove function  <br />
f:\mathbb{C}\longrightarrow\mathbb{C} defined by  f(z) = z^{2}+z is differentiable everywhere in  C using derivative as a limit

    Is this asking me to use first principles to show this?

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  2. #2
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by piglet View Post
    Im trying to prove function  <br />
f:\mathbb{C}\longrightarrow\mathbb{C} defined by  f(z) = z^{2}+z is differentiable everywhere in  C using derivative as a limit

    Is this asking me to use first principles to show this?

    It sounds like you're supposed to write the definition of derivative in terms of a limit, then plug in f(z), then show that the limit exists for all z in C.
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  3. #3
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    Yes, show that \lim_{h\to 0}\frac{(z+ h)^2+ (z+h)- (z^2+ z)}{h} exists.
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