(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:
(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
