L'hospital rule

  • Thread starter teng125
  • Start date
  • #1
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anybody knows how to solve this using L'hospital rule pls
(cot x) ^ sin2x with limi X to zero
 

Answers and Replies

  • #2
TD
Homework Helper
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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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