Given the Laplace transfer function H(jw)=(2wj)/(4wj+10000), when the frequency "w" becomes very large, is the Hmax=1/2?

Could anyone help to confirm this?

 

\(
H(jw) = \frac{2wj}{4wj+10000}
\)

As w gets very large, the 4wj term in the denominator will become very large as well. It will get to the point where it is much larger than 10000 and it will 'appear' as if the response is:

\(
H(jw) = \frac{2wj}{4wj} = \frac{1}{2}
\)

 

\(
H(jw) = \frac{2wj}{4wj+10000}
\)

As w gets very large, the 4wj term in the denominator will become very large as well. It will get to the point where it is much larger than 10000 and it will 'appear' as if the response is:

\(
H(jw) = \frac{2wj}{4wj} = \frac{1}{2}
\)

Thank you. It seems I've forgot the math.