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Limit with big O notation

  1. Dec 19, 2012 #1
    lim (e^x-sin(x)-cos(x))/(e^(x^2)-e^(x^3)), x->0
    = lim (1+x+o(x)-x+o(x)+1/2(x^2)-1+o(x^2))/((x^2)+1+o(x^2)-1-(x^3)+o(x^3)), x->0
    = lim 1/2(x^2)/(x^2+o(x^2)), x->0 = 1/2
    is it correct?
  2. jcsd
  3. Dec 19, 2012 #2


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    Staff: Mentor

    You cannot simplify o(x)+1/2 x^2 to 1/2 x^2, as o(x) could (and does in your example!) include terms of x^2. You have to expand it more.
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