Solve: Power Series Expansion
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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 and show the accurate and approximate values of f(0.02) stating the difference between accurate and approximate values.
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The sound wave is given by the following function:
f(t) = 0.5e^(-2t) cos 4t
Power Series Expansion of e^x is given as follows:
e^x=1+x+x^2/2!+x^3/3!+x^4/4!+⋯
Putting x = (-2t) in the above ...
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