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anonymous

  • one year ago

How do you approach this one? equation coming ...

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  1. anonymous
    • one year ago
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    Come up with a reasonably accurate estimate of \[\int\limits_{1}^{\infty} \frac {e^{-x}}{ \sqrt{1+ x^{4}}} dx\]

  2. anonymous
    • one year ago
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    Can you just say that 1/E^x will dominate?

  3. ganeshie8
    • one year ago
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    An estimation w/o knowing the amount of error is useless

  4. dan815
    • one year ago
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    you could expand e^-x to a few terms in taylor series

  5. dan815
    • one year ago
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    and state what the error is wrt to how many terms u expand upto

  6. anonymous
    • one year ago
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    Im not sure what you mean Dan..sorry.. If 1/E^x is dominant then the function is heading to 0 is there some way of just using the fundamental formula here? If I plot this function it seems to zero out by the time it hits 15, what if I integrate and then just do something like If f'[x] = Power[E, -x]/Sqrt[1 + x^4] Then the integration of f'[x] is f[15] - f[1]

  7. anonymous
    • one year ago
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    and I get 1.903373417798832 * 10^-8

  8. dan815
    • one year ago
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    |dw:1438279836414:dw|

  9. dan815
    • one year ago
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    |dw:1438279964137:dw|

  10. dan815
    • one year ago
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    u can use those other approximation methods u are doing there too

  11. anonymous
    • one year ago
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    Okay.. so I don't know if this will be correct but after concluding that the dominant term 1/E^x will approach zero, then examining the plot and seeing that the function approaches zero by about x=15, then taking the definite integral over several intervals of [1,15] [1,30] [1,100] , then I found to within 3 decimal places, the function converges upon 0.127

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