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Question on limits

 
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heo83



Joined: 07 Jul 2004
Posts: 29
Helped: 2


Post02 Aug 2004 17:15   Question on limits

I have this exercise:

         
      1 - [cos(x)]^sin(x)
lim --------------------- = ?????
x->0 tan(x)^3

(explain to someone that would be confused by these formulas: cos(x) to the power of sin(x), tan(x) to the power of 3)

Does anyone have the solution, please post it. Thanks a lot.
Besides can you explain it in details ?
Something like
>limit((1-cos(x)^sin(x))/tan(x)^3, x = 0); is not welcome. (that means I can use Maple, or computer to solve this exercise, to have the numeric value but I want to understand why and how?)
To me:
I tried to use l'Hospital but diff(cos(x)^sin(x),x) would cause a lot things relate to log that could make this exercise more difficult. Halt!
Crying or Very sad Crying or Very sad
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zorro



Joined: 06 Sep 2001
Posts: 319
Helped: 34


Post02 Aug 2004 19:43   Re: Question on limits

Express cos(x) as exp(ln(cos(x)); then cos(x)^sin(x)=exp(sin(x)*ln(cos(x))).
Then apply L’Hopital rule twice for solve the indetermination.
The result is 1/2 .

Z
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