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.

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.