Fall 2012 Math 152 Group Activity 13 (§10.9, 11.1) Section ________ Names ____________________ Calculators are not allowed. Problems: √ . 1. Consider the function nd
(a). Find the 2 degree Taylor polynomial |
For 1
!
|
. 3 (which contains ) together with the Taylor inequality (b). Consider the interval 1
|
at |
over this interval, where max
|
| . |
√ , use this inequality to find a number such that |
, 3 . 2. (a) Use the Maclaurin Series representation for sin
to write sin
as an infinite series. (b) Using the series found in part (a), find the sum of the first three nonzero terms to estimate sin
. Give an upper bound on the error. 3. Find the radius and center of the sphere Solutions: 1. (a) ________________________________________ (b) ________________________________________ 2. (a) ________________________________________ (b) ________________________________________ 3. ___________________________________________ 4
2
6
11 .