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Math Help - taylor expansion

  1. #1
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    taylor expansion

    Calculate the first 5 terms of the taylor expansion of e^x about x=0.


    Use the first four terms of the above expansion to approximate e^0.5. Answer to 6 d.p.


    Finally, use the final term to estimate the error in your approximation. Answer to 3 sig figures.
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  2. #2
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    Quote Originally Posted by mr_motivator View Post
    Calculate the first 5 terms of the taylor expansion of e^x about x=0.


    Use the first four terms of the above expansion to approximate e^0.5. Answer to 6 d.p.


    Finally, use the final term to estimate the error in your approximation. Answer to 3 sig figures.
    Apply the formula: Maclaurin Series -- from Wolfram MathWorld

    Please show what work you've done. Where are you stuck?
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  3. #3
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    Alright, well the Taylor series expansion for a function f(x) about the point x = a is given by:

    f(x)=f(a)+(x-a)\frac{\partial}{\partial x} f(a) + \frac{(x-a)^{2}}{2!} \frac{\partial^{2}}{\partial x^{2}} f(a) + ...

    So in your case,

    f(x) = e^{x}

    and

    a = 0.

    so using the above formula, the first two terms are:

    f(a) = e^{0} = 1
    (x-a)\frac{\partial}{\partial x} f(a)= (x-0)\frac{d}{dx}(e^{0}) = x

    And you can find the remaining three in that same way...
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