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If \( \mathrm{L}=\lim _{n \rightarrow \infty} \frac{1}{n^{4}} \prod_{i=1}^{2 n}\left(n^{2}+i^{2}\right)^{\frac{1}{n}} \), then \( \ln L \) is equal to :
\( \mathrm{P} \)
W
(1) \( \ln 2+\frac{\pi}{2}-2 \)
(2) \( 2 \tan ^{-1} 2-4+2 \ln 5 \)
(3) \( 2 \tan ^{-1} 2+4+2 \ln 5 \)
(4) \( 2 \ln 5-4-2 \tan ^{-1} 2 \)
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