(1)  

We will first find the limit of the natural log of the expression
and then the above will be e raised to the power of the result.

(2)  



Since (A)   and , and
      (B)  

we can use L'Hopital's rule since it has the form .

We need to take the derivative of the numerator and the denominator:

Derivative of numerator:

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.

     
     
     
     

     (multiply by  to make use of identity sin(2x)=2sin(x)cos(x):
     

Derivative of denominator:  

So (2) becomes:



Use L'Hopital's rule again:

 (divide top and bottom by 2)


 

Use L'Hopital's rule again:





Divide top and bottom by 2



Use L'Hopital's rule once more:



No don't need to bother simplifying that, because we can just substitute
x=0



Therefore the log of the answer is , which means:






Edwin