Having a bit of trouble with Taylor Polynomials.
I understand the concept, but something isn't clicking.
The general equation for a Taylor Polynomial is
f(a)+f'(a)(x-a)^1+(f''(a)/2!) and etc...
I've got a problem in my book as follows...
SqRt.(1+x)
So, first term is 1... [0th term]; 1/1
Second term should be f'(0) [1]/1!*(x-0)^1 [x].
I know this is flawed.... [see below]
Any reason why?
Now, what I'm not getting...
1) Why does it alternate?
2) Bob (Back of the Book) says 1-x/2+x^2/8-x^3/16... and so on.
Anyone mind showing me how to arrive at this conclusion?
I usually pick these things up quickly, there just aren't any decent examples in my book to model after.
Thanks.
--Trevor
I understand the concept, but something isn't clicking.
The general equation for a Taylor Polynomial is
f(a)+f'(a)(x-a)^1+(f''(a)/2!) and etc...
I've got a problem in my book as follows...
SqRt.(1+x)
So, first term is 1... [0th term]; 1/1
Second term should be f'(0) [1]/1!*(x-0)^1 [x].
I know this is flawed.... [see below]
Any reason why?
Now, what I'm not getting...
1) Why does it alternate?
2) Bob (Back of the Book) says 1-x/2+x^2/8-x^3/16... and so on.
Anyone mind showing me how to arrive at this conclusion?
I usually pick these things up quickly, there just aren't any decent examples in my book to model after.
Thanks.
--Trevor