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A sound wave is given by the function

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3. A sound wave is given by the function
f(t) = 0.5e^-2t cos 4t
Write down the first four terms of the power series expansions of e^-2t and cos 4t.
Determine the cubic (up to and including the third power of t) approximation of f(t) and calculate the accurate and approximate values of f(0.02) giving your results correct to 3 decimal places.

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This solution is comprised of a detailed explanation to determine the cubic (up to and including the third power of t) approximation of f(t) and calculate the accurate and approximate values of f(0.02) giving your results correct to 3 decimal places.

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