\[
\lim _{x \rightarrow a} \frac{1}{\left(a^{2}-x^{2}\right)^{2}}\left[\frac{a^{2}+x^{2}}{a x}+\...
\[
\lim _{x \rightarrow a} \frac{1}{\left(a^{2}-x^{2}\right)^{2}}\left[\frac{a^{2}+x^{2}}{a x}+\cos \frac{\pi}{2}(a+x)-\cos \left(\frac{\pi}{2}(a-x)\right)\right]
\]
where \( a=2 m+1, m \in I \)
(a) \( \frac{\pi a^{2}+1}{16 a} \)
(b) \( \frac{\pi^{2} a+2}{8 a} \)
(c) \( \frac{\pi^{2} a^{2}+4}{16 a^{4}} \)
(d) \( \frac{\pi^{2} a^{2}+4}{32 a^{4}} \)
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