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Math Help - What is the Taylor polynomial of degree 2 for g near 8?

  1. #1
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    What is the Taylor polynomial of degree 2 for g near 8?

    Suppose is a function which has continuous derivatives, and that , , . (a) What is the Taylor polynomial of degree 2 for near ?



    I got -4-1(x-8), but it's wrong.

    (b) What is the Taylor polynomial of degree 3 for near ?



    I got -4-1(x-8) + (3/2)(x-8)^2, but it's wrong.

    (c) Use the two polynomials that you found in parts (a) and (b) to approximate .
    With ,
    I got -4-1(.1), but it's wrong
    With ,
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  2. #2
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    Do you understand what "degree" means? A polynomial is of degree "n" if and only if the highest power in the polynomial is n (I bet you learned that long ago!).

    4- 1(x- 8) is wrong because it is of degree 1, not 2.

    -4-1(x-8) + (3/2)(x-8)^2 is wrong because it is of degree 2, not 3.

    You seem be thinking that "degree" is the number of terms in the polynomial- it isn't. A polynomial of degree n typically has n+1 terms.
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  3. #3
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    p_{2}(x)=g(8)+\frac{g'(8)(x-8)}{1!}+\frac{g''(8)(x-8)^2}{2!}

    p_{2}(x)=-4-1(x-8)+\frac{4(x-8)^2}{2}

    p_{3}(x)=p_{2}(x)+\frac{g'''(8)(x-8)^3}{3!}

    the nth degree adds the term...

    \frac{g^n(x)(x-8)^n}{n!}
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  4. #4
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    Thanks! do you know how to do part c?

    c) Use the two polynomials that you found in parts (a) and (b) to approximate .
    With ,
    With ,
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