Word Count : 389

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We are asked to numerically differentiate ( f(x) = \sin(2x) ) at ( x = \pi/3 ) using forward, backward, and central differences with ( h = 0.1 ) and compute the absolute true error. Let’s solve step by step. --- Step 1: Define the formulas * Forward difference: [ f'(x) \approx \frac{f(x+h) - f(x)}{h} ] * Backward difference: [ f'(x) \approx \frac{f(x) - f(x-h)}{h} ] * Central difference: [ f'(x) \approx \frac{f(x+h) - f(x-h)}{2h} ] * __________ __________ _____ _______ ______ __________ ______ ______.
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