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Math Help - Limit theorem

  1. #1
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    Limit theorem

    I would appreciate some tips on this.
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  2. #2
    MHF Contributor red_dog's Avatar
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    \lim_{x\to x_0}\frac{xf(x_0)-x_0f(x)}{x-x_0}=\lim_{x\to x_0}\frac{xf(x_0)-x_0f(x_0)+x_0f(x_0)-x_0f(x)}{x-x_0}=

    =\lim_{x\to x_0}\frac{f(x_0)(x-x_0)}{x-x_0}-\lim{x\to x_0}\frac{x_0(f(x)-f(x_0)}{x-x_0}=

    =\lim_{x\to x_0}f(x_0)-x_0\lim_{x\to x_0}\frac{f(x)-f(x_0)}{x-x_0}=f(x_0)-x_0f'(x_0)
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