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Basic limits queston

  1. Oct 7, 2007 #1
    1. The problem statement, all variables and given/known data

    I'm asked to find the limit of [arctan(x)-(x)] / [arcsin(x)-(x)] as x--->0

    3. The attempt at a solution

    So I started plugging in values of x closer and closer to zero. I get:

    f(-0.05)= -1.994758
    f(-0.01)= -1.999790
    f(-0.001)= -2.000012

    f(0.05)= -1.994758
    f(0.01)= -1.999790
    f(0.001)= -2.000024

    At first (before I calculated (-0.001 and 0.001) I thought the limit was neg two, but after I calculated -.001 and .001 and got -2.000012 and -2.000024 I'm thrown off. Does the limit not exist, or is my calculator rounding wierdly.

    Any help is much appreciated.
     
    Last edited: Oct 7, 2007
  2. jcsd
  3. Oct 7, 2007 #2
    This is certainly a rounding error. The limit is -2 as u originally suspected. Here are some closer results:
    f(0.001)=−1.995808383
    f(-0.001)=−1.995808383
     
  4. Oct 7, 2007 #3
    so did I compute it wrong? or is that just the way my calculator rounds it?
     
  5. Oct 7, 2007 #4
    btw, thank you
     
  6. Oct 7, 2007 #5
    Arcsine and Arctan are relatively complex functions, and handheld calculators don't have the capability of doing a)operations with those complex numbers b)dividing them c)and worse of all, with really really small input values. So it is the way your calculator rounds.
     
  7. Oct 7, 2007 #6
    thank you for the help
     
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