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    So the question is to determine the Maclaurin series up to term in x^3. I'm stuck on one particluar one. I keep feeling this has clicked then get set back.

    (1 + x)*e^-x

    So I have worked out the differentials
    (1+x)*e^-x
    -xe^-x
    (x-1)*e^-x
    -(x-2)*e^-x

    Subbed in for when x = 0
    1
    -e^-1
    e^-2
    e^-1

    And then put it into the formula for Maclaurin series but I am going wrong somewhere because it isn't the right answer. Any help is appreciated thanks. I don't know if i'm starting off wrong on this on or halfway....
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    (Original post by RHCPfan)
    So the question is to determine the Maclaurin series up to term in x^3. I'm stuck on one particluar one. I keep feeling this has clicked then get set back.

    (1 + x)*e^-x

    So I have worked out the differentials
    (1+x)*e^-x
    -xe^-x
    (x-1)*e^-x
    -(x-2)*e^-x

    Subbed in for when x = 0
    1
    -e^-1
    e^-2
    e^-1

    And then put it into the formula for Maclaurin series but I am going wrong somewhere because it isn't the right answer. Any help is appreciated thanks. I don't know if i'm starting off wrong on this on or halfway....
    Huh? Subbing in x = 0 you should get
    1
    0
    -1
    2
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    (Original post by RHCPfan)
    So the question is to determine the Maclaurin series up to term in x^3. I'm stuck on one particluar one. I keep feeling this has clicked then get set back.

    (1 + x)*e^-x

    So I have worked out the differentials
    (1+x)*e^-x
    -xe^-x
    (x-1)*e^-x
    -(x-2)*e^-x

    Subbed in for when x = 0
    1
    -e^-1
    e^-2
    e^-1

    And then put it into the formula for Maclaurin series but I am going wrong somewhere because it isn't the right answer. Any help is appreciated thanks. I don't know if i'm starting off wrong on this on or halfway....
    Your differentials are correct.

    f(x)=(1+x)\cdot e^{-x}=e^{-x}+xe^{-x}
    f'(x)=-e^{-x}+e^{-x}-xe^{-x}=-xe^{-x}
    f''(x)=-e^{-x}+xe^{-x}
    f'''(x)=e^{-x}+e^{-x}-xe^{-x}

    but when you sub in x=0, there shouldn't be any e terms because e^0=1
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    (Original post by 13 1 20 8 42)
    Huh? Subbing in x = 0 you should get
    1
    0
    -1
    2
    (Original post by RDKGames)
    Your differentials are correct.

    f(x)=(1+x)\cdot e^{-x}=e^{-x}+xe^{-x}
    f'(x)=-e^{-x}+e^{-x}-xe^{-x}=-xe^{-x}
    f''(x)=-e^{-x}+xe^{-x}
    f'''(x)=e^{-x}+e^{-x}-xe^{-x}

    but when you sub in x=0, there shouldn't be any e terms because e^0=1
    Oh man I've just seen where I have gone wrong! Thank you both!! Saying I was subbing x=0 when I was doing 0,1,2. It's been a long day haha.
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    (Original post by 13 1 20 8 42)
    Huh? Subbing in x = 0 you should get
    1
    0
    -1
    2
    (Original post by RDKGames)
    Your differentials are correct.

    f(x)=(1+x)\cdot e^{-x}=e^{-x}+xe^{-x}
    f'(x)=-e^{-x}+e^{-x}-xe^{-x}=-xe^{-x}
    f''(x)=-e^{-x}+xe^{-x}
    f'''(x)=e^{-x}+e^{-x}-xe^{-x}

    but when you sub in x=0, there shouldn't be any e terms because e^0=1
    Oh man I've just seen where I have gone wrong! Thank you both!! Saying I was subbing x=0 when I was doing 0,1,2. It's been a long day haha.
 
 
 
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