Word Count : 639

---

To approximate \( f(1.5) \) using Stirling's central difference formula, we will use the given data points centered around \( x_0 = 1.6 \). Stirling's formula is particularly useful for interpolation near the middle of a set of equidistant points. --- ### Step 1: Organize the data The given data is: \[ \begin{array}{|c|c|c|c|c|c|} \hline x & 1.0 & 1.3 & 1.6 & 1.9 & 2.2 \\ \hline f(x) & 0.7651977 & 0.6200860 & 0.4554022 & 0.2818186 & 0.1103623 \\ \hline \end{array} \] We choose \( x_0 = 1.6 \) as the central point. The step size \( h = 0.3 \) (since \( x \) values are spaced by 0.3). --- ### Step 2: Construct the difference table We compute the forward differences (\( \Delta \)), second ____ _______ _________ _________ _________ __________ ______ _____ _______ ____ ________ _______.
________ _____ _________ _______ _____ __________ _______ __________ _________.
______ ____ ___ _________ ___ _________ _____ _____ _______.
____ _______ ______ ______ ____ _____ _________ __________ ____ ___.
_________ _______ ______ _______ __________.
___ ____ _________ ________ _______.
____ ___ _________ ________ __________ ____ ______ _______.
____ ___ _____ ___ ______ ___.
_____ ________ ___ _____ __________ _________.
___ ______ ____ ________ ______ ______.
___ _________ ______ ____ ___ _______ ______ _______ _________.
_______ _______ _______ __________ _____ ________ _________ ________.
________ ______ _____ ___ _______ _____.
______ __________ __________ _________ ________ ________ ___ _____ _______ ______.
_______ ______ _______ ______ _______ ______ ______ ___.
___ ________ __________ ________ _________ ________ _________ ________.
____ ______ _____ __________ ____.
___ ______ ________ ___ _________ _______ ______.
_______ _______ __________ ______ ______ ____ ____ ___ _______ ___.
_____ ____ _____ ______ __________ ___.
____ __________ ______ ___ _______ _______.
_____ ________ __________ ____ ________ ______ ______ _____.
___ ______ ____ __________ _______ _________ ___ ______.
_____ __________ _____ _______ ______ ____.
_____ ______ __________ ____ _____ _____ _____ ___ ____ ____ ___.
_____ ________ _______ _______ ______ _______ ________ _____ ________ ______ ____.
________ __________ _________ _____ _____ _________ ___ ___ _____ ________.
_________ _________ ___ ______ ______ __________ _______ ____ _______ ___.
___ _____ ______ __________ _________ ____.
_______ _________ ______ ___ _____.
_______ __________ _______ _____ ______ _________ _________ ____ _______ _____ ___ ____.
________ __________ ____ ___ ________ __________ __________ __________ ____ ____ _____.
_______ ______ ________ _________ _________ ______ _____ __________ _______ ____ ____.
____ ___ _______ ________ _________ ________ ___.
_______ ______ _____ _________ ___ ____ ____ ____ _____ __________.
________ ________ ____ ______ ______ ______ ________ __________.
___ ________ __________ ___ ___ _______.
______ _______ _________ ______ ________ ________ _______ _______ ____.
_________ ____ _____ ______ _______ _________.
_____ _____ ____ ______ __________ ____ ______ ______ _____ _________.
___ __________ ___ ____ ________ ___ _____.
___ _________ ________ _______ ____ __________ ______.
_______ _____ _________ _________ _________ _____ ______ ________ ______.
_______ _____ ________ _________ __________ _____ _________ __________ _________.
___ ___ ____ ________ _____ _________ ___.
________ _______ ___ ______ ___ ___ ____ ________ _______ ___ ______ _____.
____ ___ ________ __________ ________ ________ ___ ________ _______ _______ _____ _____.
_______ _______ _______ _________ _____.
__________ ______ ________ ________ _______ __________ ______ ____ ______ ________ ______ ______.
_____ ________ _________ _____ _________ ___ ___ ________.
_____ ________ ____ ___ _________ ______ ______ _______ _________ ________ _______.
__________ ______ ________ _______ ____ ___.
________ _________ _______ _________ ___ ____ ______ ______ ___ ________ _______.
________ ___ ______ ______ _____ ___.
_______ ______ ________ ______ ___ _______ _____ __________ _________ ____.
_____ ________ ______ __________ ______ ______.
_______ __________ _______ ____ _____ ______ _______ ______.
_______ ______ __________ _______ _______ ______ ____ ________ ______.
__________ _____ _____ __________ _____ ___ _________ ____ __________ _______ _________ _____.
____ ___ ________ ______ ________.
___ ____ ________ _________ _________ ____ _________ _________.
_________ ________ ____ __________ _____ _______ ______ _____.
Get Full Answer on WhatsApp