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M asked in Science & MathematicsMathematics · 8 years ago

Find the Taylor polynomial T3(x) for the function f centered at number a?

f(x)=e^-4x*sin2x, a=0

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  • kb
    Lv 7
    8 years ago
    Favorite Answer

    Using the familiar series for exp and sine,

    e^(-4x) sin(2x)

    = (1 + (-4x) + (-4x)^2/2! + ...) ((2x) - (2x)^3/3! + ...)

    = (1 - 4x + 8x^2 + ...) (2x - (4/3)x^3 + ...)

    = 2x - 8x^2 + (16 - 4/3)x^3 + ...

    = 2x - 8x^2 + (44/3)x^3 + ...

    So, T₃(x) = 2x - 8x^2 + (44/3)x^3.

    I hope this helps!

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