Question

taylor series of f(x)=sin(x), a=pi/2

Answer 1

since sin(x+pi/2) = cos(x) id assume its the taylor of cos(x)

Answer 2

I also need to find the radius of convergence.

Answer 3

the radius is infinity

Answer 4

can you tell me why/how?

Answer 5

first step in constructing a series so to write out the derivative for a while; and solve them for the given a; these become your corrdinants in teh series

Answer 6

essentially, your constructing a polynomial that moves the same way the function does

Answer 7

when 2 functions bend and move the same (have the same derivatives) they match up along certain conditions

Answer 8

\[f(x)=g(x)\text{ when } f'(x)=g'(x); ...;f^{(n)}{x}=g^{(n)}{x}\]

Answer 9

okay thank you!

Answer 10

can you please help me with another if I post one more?

Answer 11

i can try