Question

Find T4(x), the Taylor polynomial of degree 4 of the function f(x)=arctan(11x) about x=0.

Answer 1

how far did you get

Answer 2

we need f ' (x), f ' ' (x) , f ' ' ' (x)

Answer 3

the derivative of arctan x is 1/ (x^2+1)

Answer 4

one sec

Answer 5

11 x-(1331 x^3)/3+(161051 x^5)/5-(19487171 x^7)/7+(2357947691 x^9)/9

Answer 6

I think then
T4(x) = 11 x- (1331 x^3)/3

Answer 7

Taylor series for arctan(u) is
u-u^3/3+u^5/5-u^7/7+u^9/9-u^11/11+... (Taylor series)

Then plug in u = 11x