Taylor's Expansion of sin(x)

SoSolid

SoSolid

SoSolid

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Is there two slightly different ways of expressing the taylor expansion as I have found a slightly different template to the one my teacher has used. Can anyone help me clear this matter up, in his solution he has included some
(x-a) thing where as I am used to just writing:

f(x+h) = f(x) + f ' (x)h + f ' ' (x)h^2 / 2! + . . . . . . .
 
SoSolid said:
Is there two slightly different ways of expressing the taylor expansion as I have found a slightly different template to the one my teacher has used. Can anyone help me clear this matter up, in his solution he has included some
(x-a) thing where as I am used to just writing:

f(x+h) = f(x) + f ' (x)h + f ' ' (x)h^2 / 2! + . . . . . . .
Click to expand...
Taylor's expansion is about x=a and you have (x-a), (x-a)^2, ... instead of the h, h^2 you have. What you have is the special case where the expansion is about x=0 (called a Maclaurin series).
 
DaveF said:
Taylor's expansion is about x=a and you have (x-a), (x-a)^2, ... instead of the h, h^2 you have. What you have is the special case where the expansion is about x=0 (called a Maclaurin series).
Click to expand...

But my book specified that as the Taylor's expansion, it had one for the maclaurin and then underneath it had the Taylor's expansion, i know that the Maclaurin expansion is basically taylors about x=0. I am really confused, I understand Maclaurin but keep getting taylors wrong.
 
Well there's the Taylor and the McLaurin Series (which is really just a special case of the Taylor Series by setting a=0)

I suspect his formula is of the form:


f(x) = f(x-h) + f' h(x-h) + (f''(h)/2 )*(x-h)^2 ?
 
M0KUJ1N said:
Well there's the Taylor and the McLaurin Series (which is really just a special case of the Taylor Series by setting a=0)

I suspect his formula is of the form:


f(x) = f(x-h) + f' h(x-h) + (f''(h)/2 )*(x-h)^2 ?
Click to expand...

Yeh that is correct, but why does my book show it as the form I specified in the original post?
 
SoSolid said:
But my book specified that as the Taylor's expansion, it had one for the maclaurin and then underneath it had the Taylor's expansion, i know that the Maclaurin expansion is basically taylors about x=0. I am really confused, I understand Maclaurin but keep getting taylors wrong.
Click to expand...
Somewhat impossible for me to comment on what it says in a book without you giving more details, and it is always going to be confusing here where you can't write maths properly. What is the difference between the forms it gives for Maclaurin and Taylor?

If you want a reliable source, the wiki entry: http://en.wikipedia.org/wiki/Taylor_series seems perfectly accurate to me at first glance.
 
DaveF said:
Somewhat impossible for me to comment on what it says in a book without you giving more details, and it is always going to be confusing here where you can't write maths properly. What is the difference between the forms it gives for Maclaurin and Taylor?

If you want a reliable source, the wiki entry: http://en.wikipedia.org/wiki/Taylor_series seems perfectly accurate to me at first glance.
Click to expand...

Ok thanks, I think perhaps I just confused myself. I will use the standard template as shown on Wikipedia.
 
SoSolid said:
Yeh that is correct, but why does my book show it as the form I specified in the original post?
Click to expand...

At first glance I suspect it's simply a re-arrangement of the formula:

the first term in the form you've quoted is f(x+h)=... rather than f(x)=....
 
Yeh I think the different template I am using has something to do with the
f(x+h) at the beginning hence why the template is slightly different to the
f(x) version.

I seem to remember you can express taylors expansion in any one of the two formats.
 
SoSolid said:
Yeh I think the different template I am using has something to do with the
f(x+h) at the beginning hence why the template is slightly different to the
f(x) version.

I seem to remember you can express taylors expansion in any one of the two formats.
Click to expand...
Yes. (To be honest, I didn't notice the details of what you'd written in the first post and thought it was the Maclaurin expansion when it isn't. I hate reading ASCII maths...)
 
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