I understand Taylor polynomials, and I know what the taylor polynomial of degree

Question

I understand Taylor polynomials, and I know what the taylor polynomial of degree 10 of f(x) = ln (1+x) at a =0. I can write out the first ten terms if need be, using The sum of n = 1 to infinity of (-1)^n+1 * (x^n)/n plugging in n =1 up to n=10 will give me ten terms in a series etc....

Now allowing for that basic knowledge, I need help understanding and doing the following problem:

If you wish to answer this, I need detailed step-by-step so I can see exactly what you are doing to arrive at solution.

Explanations for why a step is being done is important.

Explanation / Answer

T = x - x^2/2 + x^3/3 - .. -x^10/10 Error term is approx x^11/11 ~ 0.001 This approximation is within 0.001 of the right answer when x < 0.6636 I hope this will help.

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