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Math Help - find the functions f and g such that

  1. #1
    Super Member bigwave's Avatar
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    Cool find the functions f and g such that

    find the functions f and g
    <br />
\lim_{x \to c}{f(x)} = \infty and \lim_{x \to c}{g(x)} = \infty

    but

    \lim_{x \to c}{[f(x) - g(x)]} \ne 0
    Last edited by bigwave; January 18th 2010 at 10:16 PM. Reason: latex error
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by bigwave View Post
    find the functions f and g
    <br />
\lim_{x \to c}{f(x)} = \infty and \lim_{x \to c}{g(x)} = \infty

    but

    \lim_{x \to c}{[f(x) - g(x)]} \ne 0
    f(x)=\frac{2}{x-1},g(x)=\frac{1}{x-1},c=1

    EDIT: Actually, to be one-hundred percent accurate you should actually consider |f(x)|,|g(x)|
    Last edited by Drexel28; January 18th 2010 at 10:28 PM.
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  3. #3
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    If you want a finite limit for the difference you could consider f(x)=\frac{ax^2}{x^2-1} and g(x)=\frac{a}{x^2-1} then f(x)-g(x)=a\frac{x^2-1}{x^2-1} \rightarrow a
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  4. #4
    Super Member bigwave's Avatar
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    looks like there are multiple answers to this

    what would be the simplest version of \frac{1}{x} that could be used with this. in that it looks like we must have an x in the denominator.
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