Question

How can i verify the accuracy of this Taylor polynomial approximation:

Answer 1

i pretty much get everything up till the graph, what does this graph tell us about how many digits are trustworthy

Answer 2

You'd need to use the Error Formula, explicitly stated using little-oh notation:
\[
R_k(x)=o\left(|x-l|^k\right)\\
x\to a
\]If the function stated below is not the same as the one above, or even if it is, this should still apply.

Answer 3

okay. But do you now what is going on with the graph, what does it tell us?