Homework Soursea Give the fourth degree Taylor polnomial for fx sin x cente
a) Give the fourth degree Taylor polnomial for f(x) =sin (x), centered at a = pi/2.
b) If T4(x) is the Taylor polynomial you computed in part (a), use Taylor\'s inequality to estimate the accuracy of the approximation sin(x) =T4(x) on the interval [ pi/3, 2pi/3].
b) If T4(x) is the Taylor polynomial you computed in part (a), use Taylor\'s inequality to estimate the accuracy of the approximation sin(x) =T4(x) on the interval [ pi/3, 2pi/3].
Solution
1-1/2 (x-pi/2)^2+1/24 (x-pi/2)^4+O((x-pi/2)^6) see this : http://www.wolframalpha.com/input/?i=taylor+polynomial+sin%28x%29%2C+a+%3D+pi%2F2
