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Math Help - Finding Limits in a Rational Expression Containing Two Variables

  1. #1
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    Finding Limits in a Rational Expression Containing Two Variables

    The question I am stuck on is:

    lim sp (x+h) x
    h→0 spc h


    I know that h=0 is undefined because that would make the denominator 0. I also know that if I sub 0 in to solve the limit algebraically, I get 0 as a numerator as well, which I know is indeterminate form.

    The problem is, I am not sure how to further factor in order to get h out of the denominator, or if there is even a limit. My textbook says that most often indeterminate form suggests that there is a limit. I am just unsure as to what I should do next.

    As for background information, I am new to these topics but generally catch on well enough. I am just looking for a little direction.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Finding Limits in a Rational Expression Containing Two Variables

    Expand (x+h)^2=x^2+2xh+h^2, therefore you get:
    \lim_{h\to 0} \frac{x^2+2xh+h^2-x^2}{h}=\lim_{h\to 0}\frac{2xh+h^2}{h}=\lim_{h\to 0}\frac{h(2x+h)}{h}=...
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