Word Count : 402

---

We are asked to determine the step size $h$ for quadratic interpolation of $$ f(x) = (2 + x)^4, \quad 1 \le x \le 2 $$ so that the interpolation error satisfies $$ |E(x)| \le 10^{-6} $$ --- ### Step 1: Interpolation Error for Quadratic Lagrange Interpolation The error term for an interpolation polynomial of degree $n$ is $$ E(x) = \frac{f^{(n+1)}(\xi)}{(n+1)!} \prod_{i=0}^{n} (x - x_i) $$ ___ _________ ___ ____ ______.
_____ _______ _______ ________ ________ _________ _____ ________ ______.
________ ________ _________ ____ __________ ________ _____ ________ ______ ____ ________ ____.
_________ __________ __________ _______ _________.
___ _______ _____ ______ _______ ___ ________ ________ ________ ______.
________ _____ _________ ________ _______ ____ __________.
__________ _________ ___ ______ _______ ___ ______ ____ ___ _______ _________ ________.
_____ _____ ____ ______ ___ _____ ___ ____ ________ __________ _____ _______.
_____ ____ _________ _________ __________ ________.
_________ _______ __________ ______ _____ _____ ___.
_________ _____ _____ ______ _______ ________ ________ _________ _______ ______ _________ ________.
______ ___ _________ _____ __________ _________ ______ ______ ___ ______ ___ ______.
_____ ______ ____ __________ __________ ___ ___ ____ __________ _____ _______ _____.
_________ _____ _________ __________ ____ ___ __________ _________ _______ __________ _______.
_______ ________ ____ _______ _______ _______ ______ _________ _______ _________ _________.
_________ ________ __________ ________ __________ ______ _______.
___ ____ __________ ________ ____.
__________ ______ _____ _________ ____ _________ ________ ___.
________ ____ _________ _____ _______ __________.
________ __________ _________ ____ ___ ______ _______.
______ ______ _______ _________ _______ ___ __________ _________ ________ _________ ___.
____ _______ ___ _____ ___.
___ _________ ___ _____ ____ ________ ____ ____ ___ ___ __________.
__________ __________ __________ ________ _______.
______ __________ ______ ________ ______ ___ ___ ______ ________ ___ ________ _________.
_________ ____ ___ _________ _______ ______ ________ _______ ____ ________.
______ ___ _______ ____ __________.
____ __________ ________ _________ _______ _______.
__________ ___ ___ ___ ______ ____.
_________ _________ __________ ______ ______ _________ __________ _______.
___ _______ _____ ____ __________.
__________ _______ _____ ____ ___ _____ ___.
________ _________ ________ __________ ____ ______ ______ __________ ______ ______ ______.
_________ _________ ____ ______ ______ _________ __________ _________.
______ _____ _________ _______ __________ ______ _____ ___ ___ ______.
______ ________ ___ ____ ____ ________ ______ ________.
________ __________ _____ _______ _____ _________.
_____ _______ ____ ____ ______ ______ _____ __________ _____ ____ ___.
_______ __________ _________ _____ ______.
________ _______ _____ ___ ____.
_________ _________ _____ __________.
Get Full Answer on WhatsApp