Find the first five non-zero terms of the Maclaurin series for the product of the exponential and sine functions.

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Power Series for e^x sin x

Series of numbers core

Find the first five terms of the power series for \(e^x \sin x\).

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Tests the ability to recall standard Maclaurin series and carefully perform algebraic multiplication and collection of terms.

This is a standard exercise in Calculus II when learning how to manipulate known power series to find new ones without taking multiple derivatives.