Hey guys I am unsure how to find the error bound.
Use the langrange interpolating polynomial of degree 3 or less and four digit chopping arithmetic to approximate $\cos(.750)$ using the following values. Find an error bound for the approximation.
$\cos(.698)=.7661, \cos(.733)=.7432, \cos(.768)=.7193, \cos(.803)=.6946$
The actual value of $\cos(.750)=.7317$
I used Lagrange interpolating polynomials and got .6915
Now how would I find the error bound?
The formula for the error bound is:
$\large{f^{n+1}(\xi(x)) \over (n+1)!}*(x-x_0)(x-x_1)…(x-x_n)$
In this case the formula would be:
$\large{f^{4}(\xi(x)) \over (4)!}*(x-.698)(x-.733)(x-.768)(x-.803)$
Just not sure how to continue from here
Best Answer
You know all the derivatives of $\cos x$ are no larger than $1$, so you can just plug that in and evaluate for $x=0.750$ As the cosine function is monotonic over this range, it would seem your $0.6915$ value is wrong.