Unformatted text preview: sin( x ) 1+ x 2 near b = 0. 3. Working with Taylor’s Inequality. i. e. the error formula | T n ( x )-f ( x ) | ≤ M | x-b | n +1 ( n + 1)! (a) Find an upper bound for the error in approximating e x using the 4 th Taylor polynomial about 0 for x in the interval [-. 2 , . 2]. (b) Find an upper bound for your error in 1(d). (c) Find the second Taylor polynomial for f ( x ) = x 3 + x based at b = 1. Find an interval J around b = 1 such that the error in approximating f ( x ) using T 2 ( x ) is less than 0 . 001 for all x in the interval J . (d) Let f ( x ) = 1 5-x and b = 0. Find an integer n so that the error in approximating f ( x ) with T n ( x ) for x in the interval [-2 , 2] is smaller than 0 . 009. 1...
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This note was uploaded on 05/31/2008 for the course MATH 126 taught by Professor Smith during the Spring '07 term at University of Washington.
- Spring '07