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X^2 limit help

  1. Oct 3, 2007 #1
    1. The problem statement, all variables and given/known data
    lim as x approaches 1 from the left of (sin[tex](\sqrt{1-x})[/tex])/[tex]\sqrt{1-x2}[/tex]

    and

    lim as x approaches infinity [tex](x^{2}+sinx)/(x^{2}+cosx)[/tex]


    3. The attempt at a solution
    I have attempted to solve these although my brain is raw, i have done a hundred limits today because my assignment is due tomorrow and im just lost on these ones... any starting tips
     
    Last edited: Oct 3, 2007
  2. jcsd
  3. Oct 3, 2007 #2

    Dick

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    The second one is easy. sin and cos are bounded. x^2 isn't. Your first problem doesn't have enough parentheses in it to make it clear. But in any event, since it looks like it is of a 0/0 form I would use L'Hopital's rule. Is it sin of the whole thing or just of the first sqrt. And does x2 mean 2*x or x^2?
     
    Last edited: Oct 3, 2007
  4. Oct 3, 2007 #3
    ok i fixed the parentheses,

    What do u mean by sin and cos are bounded
     
  5. Oct 3, 2007 #4

    Dick

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    I mean |sin(x)|<=1 and same for cos while x^2 goes to infinity. Now does x2 mean x^2 or 2*x?
     
  6. Oct 3, 2007 #5
    sorry, yeah it means x^2
     
  7. Oct 3, 2007 #6

    Dick

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    I'm still going for trying to hit the first one with L'Hopital's rule. How's the second one going?
     
  8. Oct 3, 2007 #7

    Hurkyl

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    Isn't the first one just sin x / x in disguise?
     
  9. Oct 3, 2007 #8

    Dick

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    Sure it could be done that way. I'm still waiting for the OP to do SOMETHING. The second one is not that hard.
     
  10. Oct 3, 2007 #9
    I've solved the second one, i got 1, easy... just divided by the highest power of x in the denom. I did it a while ago i just for got to post sorry haha.... but the first one has still got me,, because their is an x^2 in the bottom, so its not quite sinx/x
     
  11. Oct 3, 2007 #10

    Dick

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    You can factor (1-x^2)=(1-x)*(1+x). I was wondering if I had lost you.
     
  12. Oct 4, 2007 #11
    perfect solved it, 1/root2
     
  13. Oct 4, 2007 #12

    Dick

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    Yes you did.
     
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