Calculate an error bound of this interpolation value

[JimmyJockstrap]

I attached the file. I am up to 1(c).

Would the error bound of the interpolation value just be taylor series error term?

Thanks

 

[HallsofIvy]

Yes, that's just the Taylor Series error form:
$$error< \frac{M_n}{n!}|x^n|$$
Where M_n is an upperbound on the n^th derivative between 0 and x.

 

[JimmyJockstrap]

so the 3rd derivative of ln(1+x)= 2/((1+x)^3)

And the upper bound on that between 0 and x=1, since I was solving ln(1+1), is 2?



so Mn=

so error<(2/(3!))*1^3=0.333333333333333333?

I was wondering is the error bound meant to be 0.333333333 each side or 0.3333333 overall so is it 0.1666666666666666666666 each side(ie. positive and negative) or 0.3333333333 a side so 0.66666666666666666666666 overall both sides?