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    I've spent ages trying to work out how to do these but I can't seem to see a way if anyone could point me in the right direction......

    Limx->inf (sqrt(x^2 +3x + 1 )) - 1

    Limx->0 [(2^x) - 1]/x

    I know the answer to the second one is ln2 through subbing in values likes 0.00001 etc. but can't actually get the answer, I keep getting xln2 etc.


    thanks
    dan
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    (Original post by danhirons)
    I've spent ages trying to work out how to do these but I can't seem to see a way if anyone could point me in the right direction......

    Limx->inf (sqrt(x^2 +3x + 1 )) - 1

    Limx->0 [(2^x) - 1]/x

    I know the answer to the second one is ln2 through subbing in values likes 0.00001 etc. but can't actually get the answer, I keep getting xln2 etc.


    thanks
    dan
    for 1)
    Take out x as factor from both terms (at the square root x^2)
    \displaystyle x\cdot \left( \sqrt{1+\frac{3}{x}+\frac{1}{x^2  }}-\frac{1}{x})

    for 2)
    L'Hospital
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    (Original post by ztibor)
    for 1)
    Take out x as factor from both terms (at the square root x^2)
    \displaystyle x\cdot \left( \sqrt{1+\frac{3}{x}+\frac{1}{x^2  }}-\frac{1}{x})

    for 2)
    L'Hospital
    Thanks, I don't know how/why but I typed question 1 out wrong, instead it should be minus x instead of minus 1 at the end. Should I still approach the question in the same way???
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    Try rationalising  \sqrt{x^2+3x+1}-x first.

     (\sqrt{x^2+3x+1}-x) . \frac{\sqrt{x^2+3x+1}+x}{\sqrt{x  ^2+3x+1}+x}
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    (Original post by danhirons)
    Thanks, I don't know how/why but I typed question 1 out wrong, instead it should be minus x instead of minus 1 at the end. Should I still approach the question in the same way???
    No.
    Form as Spungo wrote
 
 
 
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