Evaluate \( \lim _{x \rightarrow \infty}\left[\sqrt{a^{2} x^{2}+a x+1}-\sqrt{a^{2} x^{2}+1}\righ...

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Evaluate \( \lim _{x \rightarrow \infty}\left[\sqrt{a^{2} x^{2}+a x+1}-\sqrt{a^{2} x^{2}+1}\right] \)
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