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Math Help - Simple limit...

  1. #1
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    Simple limit...

    It's unbelievable how much and how soon I can get rust if I don't keep doing math stuff.

    I've this simple problem that I cannot resolve...

    I cannot see which of the two functions prevales.

    limit for x to 0 of [ ln(x^2) + 1/(x^2) ]

    Thanks a bunch!
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  2. #2
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    Re: Simple limit...

    Quote Originally Posted by paolopiace View Post
    It's unbelievable how much and how soon I can get rust if I don't keep doing math stuff.

    I've this simple problem that I cannot resolve...

    I cannot see which of the two functions prevales.

    limit for x to 0 of [ ln(x^2) + 1/(x^2) ]

    Thanks a bunch!
    \ln(x^2)+\frac{1}{x^2}=-\ln\left(\frac{1}{x^2}\right) +\frac{1}{x^2}

    Put y=1/x^2 then we have:

    \ln(x^2)+\frac{1}{x^2}=-\ln\left(y\right) +y

    Now \ln(y) goes to infinity as y becomes large more slowly than any polynomial in y, so eventually the y dominates and the whole thing goes to infinity with y.

    CB
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  3. #3
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    Re: Simple limit...

    Very much appreciated! Thank You...
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