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Math Help - limit problem help

  1. #1
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    limit problem help

    limit problem help-screen-shot-2012-12-13-9.37.44-pm.png


    im not good at limit problems yet, but I understand definition of a limit (with the help of the sticky on this site and paul's math notes!)

    However im not sure how to approach one like this.
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  2. #2
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    Re: limit problem help

    As the hint says, consider the two cases x<1 and x>1 separately. In the x<1 case, you want to make sure that \ln{x}>-\frac{1}{10}, so you need x > 0.905. In the x>1 case, you want to make sure that \ln{x}<\frac{1}{10}, so you need x < 1.105. In the first case, you would need to set \delta to 1 - 0.905 = 0.095 or less, and in the second case, you would need to set \delta to 0.105 or less. Since you want both to be true, choose \delta=0.095.

    - Hollywood
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