Attachment 26213

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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- Dec 13th 2012, 05:39 PMkingsolomonsgravelimit problem help
Attachment 26213

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. - Dec 14th 2012, 08:38 AMhollywoodRe: 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 $\displaystyle \ln{x}>-\frac{1}{10}$, so you need x > 0.905. In the x>1 case, you want to make sure that $\displaystyle \ln{x}<\frac{1}{10}$, so you need x < 1.105. In the first case, you would need to set $\displaystyle \delta$ to 1 - 0.905 = 0.095 or less, and in the second case, you would need to set $\displaystyle \delta$ to 0.105 or less. Since you want both to be true, choose $\displaystyle \delta=0.095$.

- Hollywood