Taylor/MacLaurin polynomials

intervade · Apr 11, 2010

1. The problem statement, all variables and given/known data

Find a Taylor or Maclaurin polynomial to apporximate ln(1.75) using 6 terms.

2. Relevant equations

3. The attempt at a solution

I now that a MacLaurin polynomial is as follows.. c=0

$)+f%27(c)x+\frac{f%27%27(c)}{2!}x^{2}+\frac{f%27%27%27(c)}{3!}x^{3}+...+\frac{f^{n}(c)}{n!}x^{n}.gif$

and a Talyor polynomial is as follows..
$frac{f%27%27(c)}{2!}(x-c)^{2}+\frac{f%27%27%27(c)}{3!}(x-c)^{3}+...+\frac{f^{n}(c)}{n!}(x-c)^{n}.gif$

so do I assume I'm working with ln(x)? I'm not really sure where to go with a value.. I have worked with questions such as.. estimate the sin(x) with a 5th degree taylor polynomial.. but this is a little bit different, maybe someone can push me in the right direction!

Count Iblis · Apr 11, 2010

You can expand around a point where the function is sufficently often differentiable. So, you cannot expand around the point x = 0 (i.e. take c = 0, as Log(x) is undefined there and certainly not differentiable at that point), but you can expand around x = 1.

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Taylor/MacLaurin polynomials

intervade

Count Iblis

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