So I set $f(x)=\sqrt{1+x}$ and then went on to estimate the error for $x=0.1$ according to the Lagrangian formula will be $$\frac{f^{n+1}(ξ)*0.1^{n+1}}{(n+1)!}.$$ I know $0<ξ<0.1$ but I still cannot think of how to bound my error. I did think that all of the derivatives will have the x in the denominator so the largest value for each derivative would be for ξ=0.1 but that still does not help me bound my error.
Can I just use that they will all be less than 1 (since x is in the denominator and the coefficient keeps becoming smaller for each derivative) or is this really off?
Please explain how to bound the error when the function is not sinx or cosx. Thanks.