- #1
Badmouton
- 7
- 0
I have to find the Maclaurin series of:
(1) f(x)=cos(x)+x,
(2) g(x)= cos(x^2)+x^2
(3) h(x)=x*sin(2x).
I'm stuck at the first one, I kind of understand the concept of how P(0)=f(0)+f'(0)x+(f''(0)x^2)/2+. . .
What it gave me when I started calculating the value of the fn was this:
f(0)=cos(0)+0=1
f'(0)=-sin(0)=0
f''(0)=-cos(0)=0
And the pattern kept repeating as follows: 1,0,-1,0,1,0,-1,0.
So when I want to write the mclaurin series, should it come out as?
P(x)=Ʃ(x2n(-1)n)/n!
As for the other problems, I really don't know how to start
(1) f(x)=cos(x)+x,
(2) g(x)= cos(x^2)+x^2
(3) h(x)=x*sin(2x).
I'm stuck at the first one, I kind of understand the concept of how P(0)=f(0)+f'(0)x+(f''(0)x^2)/2+. . .
What it gave me when I started calculating the value of the fn was this:
f(0)=cos(0)+0=1
f'(0)=-sin(0)=0
f''(0)=-cos(0)=0
And the pattern kept repeating as follows: 1,0,-1,0,1,0,-1,0.
So when I want to write the mclaurin series, should it come out as?
P(x)=Ʃ(x2n(-1)n)/n!
As for the other problems, I really don't know how to start