Question

Hello! I am struggling with this problem:

Find the Taylor Series for sin(x-2) centered at c=3.

My work so far:
sin(1)+(x-3)cos(1)-(1/2)(x-3)^2sin(1)-(1/6)(x-3)^3cos(1)+(1/24)(x-3)^4sin(1)...
I know that the Taylor series for sign is typically: the summation from n=0 to infinity of ((-1)^n)/((2n)!) (x-c)^2n

I would appreciate any help! Thanks!

Answer 1

looks good to me.

Of course, the series is

∞
∑ 1/k! f^{^(k)} (x-2)^{^k}

The (2n)! series is for cos(x)
k=0