Please help. I got stuck on this problem all week. And please show steps. Use Taylor Inequality to estimate approximation f(x)Tn(x) when x lies in the given interval. Round your answer to six decimal places. a=3, n=3, 2.5<=x<=3.5?

Answer 1

well, the formula is
|R_k(x)| <= M/(n+1)! |x-a|ⁿ⁺¹

Now, 2.5 <= x <= 3.5 means |x-3| <= 1/2

Using your values, that means that
|R₃(x)| <= M/4! * 1/16
where M is a bound on the 4th derivative of f(x), which you have not specified, but maybe you can fix that

Answer 2

The function is f(x)=ln(1+2x) but the 4th derivative I don't know. So, how do I plug in now?