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Trigo Limit Type 0/0

  1. Jul 15, 2011 #1
    1. The problem statement, all variables and given/known data
    Find limit of (sin x - x)/(x - tan x) as x approaches zero

    2. Relevant equations
    Type 0/0 , use L'Hopital's rule, differentiate.

    3. The attempt at a solution
    Every time I apply the rule it gets more complicated

    (cos x - 1)/(1 - sec^2 x)
    (sin x)/(2 sec^2 x tan x)
    (cos x)/(2 Sec^4 [x] - 4 Sec^2 [x] Tan^2 [x])

    etc etc please help
  2. jcsd
  3. Jul 15, 2011 #2
    Stop here, write sec and tan in terms of sin and cos. Eliminate sin from numerator en denominator.
  4. Jul 15, 2011 #3
    Ok usually how do you decide when to stop differentiation and use alternative method?
  5. Jul 15, 2011 #4
    The idea is to simplify the formula enough after each differentiation. That way you can see that you need to stop differentiation. Here, you need to write everything in sin and cos. Then you'll see after the second differentiation that you can cancel thingies.
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