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Limes without d'hospital

  1. Mar 4, 2010 #1
    1. The problem statement, all variables and given/known data
    hello, what can I do to solve this without using d'hospital method?
    [tex]\lim_{x\to0}\frac{\tan x-x}{x^3}[/tex]
     
  2. jcsd
  3. Mar 4, 2010 #2
    Recall the formula [which is just the M.S. for tan(x)]:
    [tex]tan(x)=x+\frac{1}{3}x^3+\frac{2}{15}x^5+\frac{17}{315}x^7+...[/tex]
    Substitute this in the limit and the two "x" will be cancelled.
    Then devide the denominator and the numerator by x^3.
    and the limit will be done by the direct substitution.
    The limit = 1/3
     
  4. Mar 4, 2010 #3
    look up the taylor series for sin and cosine and write the one for tan. Now factor out X^3 from the top and take that limit as X goes to Zero
     
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