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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 ___ ___ _______ ____ _______ __________ ________ __________ _____ _____ _______.
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