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FP2: Taylor Series confusion Watch

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1. Hi,

The question I need help with is:

Use Taylor's expansion to express each of the following as a series in ascending powers of x as far as the term x^4.

A) cos(x+(pi/4))

For this one, I got the correct answer, it being:
1/root2 (1 - x - x^2/2 + x^3/6 + x^4/24...)

By using f(pi/4) and its respective deriviates.

B) Ln(x+5)

Ln5 + (1/5)x...

My issue is, this answer appears to be using the results of f(0) and further derivatives where x = 0.
Why did they not use f(5), as this contradicts part a)?
Ln10 + (1/10)x...

Thank you. I hope I managed to make myself clear

This is taken from the Edexcel textbook.
2. (Original post by JLegion)
Hi,

The question I need help with is:

Use Taylor's expansion to express each of the following as a series in ascending powers of x as far as the term x^4.

A) cos(x+(pi/4))

For this one, I got the correct answer, it being:
1/root2 (1 - x - x^2/2 + x^3/6 + x^4/24...)

By using f(pi/4) and its respective deriviates.

B) Ln(x+5)

Ln5 + (1/5)x...

My issue is, this answer appears to be using the results of f(0) and further derivatives where x = 0.
Why did they not use f(5), as this contradicts part a)?
Ln10 + (1/10)x...

Thank you. I hope I managed to make myself clear

This is taken from the Edexcel textbook.
For the first question, you have expanded about . What you've written as is in fact as the function contains a translation that leads to .

As an aside, you could, if you wished, expand the function about the point , though what you've written there is not quite correct, the second term would be , but expanding about is often easier.
3. Oh I see!

That completely makes sense now.

Thank you for all your help

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