Maths&physics
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which of the equations for Taylors series fro I use and what's my value for a and why?
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RDKGames
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(Original post by Maths&physics)
which of the equations for Taylors series fro I use and what's my value for a and why?
Isn't there only one for Taylor series?

Expansion about the point x=a is:

f(x) =f(a) + f'(a)(x-a) + \dfrac{1}{2} f''(a)(x-a)^2 + \dfrac{1}{6}f'''(a)(x-a)^3 + \ldots
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NotNotBatman
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(Original post by Maths&physics)
which of the equations for Taylors series fro I use and what's my value for a and why?
There is only one Taylor's Series for the function sec^2x.

Which is ( f(x) evaluated at a)  \displaystyle \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!}(x-a)^n and we call this Maclaurins series when evaluated at a=0.

Notice that in Taylor's series we use  (x-a) so what is a equal to in  (x-\frac{\pi}{4}) ?
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Maths&physics
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(Original post by RDKGames)
Isn't there only one for Taylor series?

Expansion about the point x=a is:

f(x) =f(a) + f'(a)(x-a) + \dfrac{1}{2} f''(a)(x-a)^2 + \dfrac{1}{6}f'''(a)(x-a)^3 + \ldots
there are different types on here: https://www.examsolutions.net/tutori...FP2&topic=1926
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(Original post by NotNotBatman)
There is only one Taylor's Series for the function sec^2x.

Which is ( f(x) evaluated at a)  \displaystyle \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!}(x-a)^n and we call this Maclaurins series when evaluated at a=0.

Notice that in Taylor's series we use  (x-a) so what is a equal to in  (x-\frac{\pi}{4}) ?
thanks, how many different types are there?
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NotNotBatman
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(Original post by Maths&physics)
thanks, how many different types are there?
The Taylor's series for a one variable function is given by the formula aforementioned, there isn't another type.
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RDKGames
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(Original post by Maths&physics)
there are different types on here: https://www.examsolutions.net/tutori...FP2&topic=1926
No, there is only one Taylor's series.

If a=0 then it's a special case of MacLaurin's series.
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NotNotBatman
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(Original post by Maths&physics)
there are different types on here: https://www.examsolutions.net/tutori...FP2&topic=1926
The point of that second example is to show that for some really small value epsilon  |a| - \epsilon = 0 you can use the taylor's series to approximate a function very close to 0, if the Maclaurins series fails (as some  \frac{g^{(n)}(0)}{n!} may not be defined). When asked to use the Taylor's series you use the one mentioned throughout this thread.
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