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Determine the coefficients to compute the first derivative of $f(x)=\sin \left(x^{2}\right)$ at $a=2$ using the points $\{a-2 h, a-h, a, a+h, a+2 h\}$. Give the estimate of the derivative as a function of $h$. Determine the best value of $h$ for the greatest accuracy of the answer. How many digits accuracy can you expect with this choice of $h$ ?
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