# Thread: limit problem help

1. ## limit problem help

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.

2. ## 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