MATH 1132Q Lecture 20: MATH 1132Q Lecture : MATH 1132Q , Lecture 20 , Section 11.11 -- Applications of Taylor Polynomials

• School: UConn
• Department: Mathematics
• Course: MATH 1132Q
• Professor: D. McArdle

Document Summary

Math 1132q , lecture 20 , section 11. 11 -- applications of taylor polynomials. The degree n taylor polynomial approximation to f(x) at x = a is: + x^5/5! (a) use the degree 3 taylor polynomial for f(x) to approximate f(. 2) = sin(. 2) = 0. 1987 (4 decimal places) (b) estimate the accuracy of this approximation. Alternating series remainder estimate error < i next term in series i = i x^5/5! Taylor"s inequality: if i f^(n+1) i m , then . I x-a i^n+1 (a) find the degree 2 taylor polynomial approximation to f(x) = e^x at x=0. T 2 (x) = 1 + x + x^2/2! (b) use taylor"s inequality to estimate the accuracy of the approximation when x lies in the interval. 0. 1 x 0. 3 n = 2 f^(n+1) (x) f^(3) (x) = e^x. Largest value of f^(3) (x) on [ -0. 1 , 0. 3 ] is at x = 0. 3 --