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Another limit using l'hopitals

  1. Jan 17, 2010 #1
    1. The problem statement, all variables and given/known data
    limit as x goes to infinity of (1/x^2) - (cscx)^2


    2. Relevant equations



    3. The attempt at a solution
    I made it so the denominator is x^2, but then it would 1-inf/inf which isn't indeterminate. i need help setting it up so it would be in indeterminate form. thanks.
     
  2. jcsd
  3. Jan 17, 2010 #2

    Dick

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    You probably mean lim x->0, right? Just make a common denominator and combine those two terms into a single fraction. It's probably easier to write 1/sin(x)^2 instead of csc(x)^2, but it will still take several derivatives before you get a nonindeterminant answer from l'Hopital.
     
    Last edited: Jan 17, 2010
  4. Jan 17, 2010 #3
    nope, the question states lim x-> inf
     
  5. Jan 17, 2010 #4

    Dick

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    Then tell me about the limiting behavior of 1/x^2 and csc(x)^2 as x->inf. Is that expression really indeterminant?
     
  6. Jan 17, 2010 #5
    that's what my original problem was
     
  7. Jan 17, 2010 #6

    Dick

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    Sketch a graph of each one. The limiting behavior should be visually obvious.
     
  8. Jan 17, 2010 #7
    The limit does not exist by any means. If needed, a proof can be given.

    AB
     
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