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Math Help - Finding the limit

  1. #1
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    Finding the limit

    Hi guys i need some help in solving this question

    the problem is:

    lim -> 0

    and the equation is:

    ((1/x+3) - (1/3))/x

    if its too messy above, basically (1/x+3) - (1/3) are all divided by 'x'.

    Obviously, if I sub x = 0 then the equation will give me 0/0, so can anyone show me how to solve this one I would greatly appreciate it.

    thanks guys
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  2. #2
    MHF Contributor red_dog's Avatar
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    \lim_{x\to 0}\frac{\frac{1}{x+3}-\frac{1}{3}}{x}=\lim_{x\to 0}\frac{\frac{3-x-3}{3(x+3)}}{x}=

    =\lim_{x\to 0}\frac{-x}{3x(x+3)}=\lim_{x\to 0}\frac{-1}{3(x+3)}=-\frac{1}{9}
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  3. #3
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    Quote Originally Posted by red_dog View Post
    \lim_{x\to 0}\frac{\frac{1}{x+3}-\frac{1}{3}}{x}=\lim_{x\to 0}\frac{\frac{3-x-3}{3(x+3)}}{x}=

    =\lim_{x\to 0}\frac{-x}{3x(x+3)}=\lim_{x\to 0}\frac{-1}{3(x+3)}=-\frac{1}{9}

    Thanks!!!
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