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Homework Help: L'hospital rule

  1. Feb 13, 2006 #1
    anybody knows how to solve this using L'hospital rule pls
    (cot x) ^ sin2x with limi X to zero
     
  2. jcsd
  3. Feb 13, 2006 #2

    TD

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    Homework Helper

    You can write:

    [tex]f\left( x \right)^{g\left( x \right)} = e^{\ln \left( {f\left( x \right)^{g\left( x \right)} } \right)} = e^{g\left( x \right)\ln \left( {f\left( x \right)} \right)}[/tex]

    So:

    [tex]\mathop {\lim }\limits_{x \to 0} f\left( x \right)^{g\left( x \right)} = e^{\mathop {\lim }\limits_{x \to 0} \left( {g\left( x \right)\ln \left( {f\left( x \right)} \right)} \right)} [/tex]

    Does this help you any further? Remember that for L'Hopital, you're trying to get 0/0 or ∞/∞.
     
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