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Integral, and limit help?

  1. Oct 16, 2007 #1
    integral, and limit help????

    well i have this integral, i have tried to solve it but got nowhere.
    it is:

    [tex]\int\frac{\1{x^3+x^2+1}[/tex]

    and the limit is
     
    Last edited: Oct 16, 2007
  2. jcsd
  3. Oct 16, 2007 #2

    EnumaElish

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    You should post this under the applicable homework help section.
     
  4. Oct 16, 2007 #3
    i am terrible with latex, so i will just write it down. Btw it is not a homework.

    integ of 1/(x^3+x^2+1)dx

    and the limit i am trying to do it without using the l'hopital rule. By the way i also would like to know if there exists any theorem which states that, if the limit of a functions can be calculated using l'hopital rule, than it will be solvable also without using l'hopital rule??

    lim{x-->0)(x cos(x)-sin(x) )/( x- sin(x) )

    thnx in advance
     
  5. Oct 16, 2007 #4
    well, no ideas on how to tackle those two problems so far???
     
  6. Oct 16, 2007 #5

    EnumaElish

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    Even if it's not "officially" homework, for this type of a problem you have a better chance of getting a response in the applicable HW section.
     
  7. Oct 16, 2007 #6
    what is the limit? you didn't write it down? and the integral using partial fractions i think
     
  8. Oct 17, 2007 #7
    well, i wrote the limit down, read post #3.
    About the integral i also think that somewhere along the way i have to use partial fractions, but how to go about factoring the denominator.??
     
  9. Oct 17, 2007 #8
    Regarding the limit, you could expand the trig terms in Taylor series and collect terms. You should find that you'll be able to divide numerator and denominator by a factor of x^3 to obtain a leading term that is your limit as x approaches zero.

    Of course, confirm your answer with L'hopital (requires three applications)
     
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