The value of \( \lim _{x \rightarrow \infty}\left(\sqrt{a^{2} x^{2}+a x+1}-\sqrt{a^{2} x^{2}+1}\...

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The value of \( \lim _{x \rightarrow \infty}\left(\sqrt{a^{2} x^{2}+a x+1}-\sqrt{a^{2} x^{2}+1}\right),(a0) \) is
(a) \( \frac{1}{2} \)
(b) \( -\frac{1}{2} \)
(c) Doesn't exist
(d) None of these
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