How do you find the Maclaurin series of the function f(x)=5cos(10x^2)?

1 Answer
Jun 6, 2015

The Maclaurin series of f_{(x)} is

f_{(x)}=f(0)+f'(0)x+{f''(0)}/{2!} x^2+{f'''(0)}/{3!} x^3+ . . .

Using this formula, get that the Maclaurin series of cos(z) is

cos(z)=1-z^2/2+z^4/{4!}+....

5cos(z)=5-5/2z^2+5/{4!}z^4+....

Substitute z=10x^2,

The Maclaurin series of 5cos(10x^2) is then

5cos(10x^2)=5-5/2(10x^2)^2+5/{4!}(10x^2)^4+ . . .