Thread: 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.

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 , so you need x > 0.905. In the x>1 case, you want to make sure that , so you need x < 1.105. In the first case, you would need to set to 1 - 0.905 = 0.095 or less, and in the second case, you would need to set to 0.105 or less. Since you want both to be true, choose .

- Hollywood