Homework for Calculus this week

I will try to figure this out...
I still at early chapter 4. But this problem is at ch 9.
It uses Taylor series, but I don't understand at all now.
I had learned this 3 or 4 years ago, but I foget almost all of it. AND I didn't do well at this part then.

Hope somebody can help me figure this out in a week. Because it's almost for sure that I can't solve this by myself.