Word Count : 268

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We are asked to find (a) and (b) such that [ \lim_{x \to 0} \frac{x(1 + a \cos x) - b \sin x}{x^3} = 1. ] First, expand (\cos x) and (\sin x) using their Maclaurin series up to the (x^3) term: [ \cos x = 1 - \frac{x^2}{2} + \dots, \quad \sin x = x - \frac{x^3}{6} + \dots ] Substitute these into the numerator: [ ____ _____ ___ _______ _______ __________ _________ _______ _____ ___ _________ _________.
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