Math 2300 Section 005 – Calculus II – Fall 2010
Quiz – Monday, November 15, 2010
We will be having a review in class every day until the next midterm exam on Wednesday of this week. For this quiz, you are given 10 minutes to decide which problems you think you can solve and which ones you want to see solved during our review session today.

Use the Lagrange Error Bound Formula for to find a reasonable bound for the error in approximating the quantity with a thirddegree Taylor polynomial for the function about . Choose the best error estimate.
Solution: We use the formula
where on the interval (i.e., the interval between where our Taylor polynomial is centered and where we're approximating the value). Since has a maximum value of on the interval , we obtain

Use the Lagrange Error Bound Formula for to find a reasonable bound for the error in approximating the quantity with a thirddegree Taylor polynomial for the function
about . Choose the best error estimate.