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SkyEscape
SkyEscape asked in Science & MathematicsMathematics · 5 years ago

Determine the Maclaurin series expansion of f(x)=exp(-x^2) and evaluate at x=1 using the first four non-zero terms in the series.?

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  • ?
    Lv 7
    5 years ago

    e^x = 1 + x + x^2 /2! + x^3/3! + x^4/4! + ............

    for x subsitute -x^2 and evaluate

    so e^-x^2 = 1 - x^2 + x^4/2! - x^6/3!

  • ted s
    Lv 7
    5 years ago

    you SHOULD already know that e^t = Σ t^n / n! ====> e^(-x²) = Σ ( -x²)^n / n! = Σ (-1)^n x^(2n) / n!...use that information

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