If \( L=\lim _{x \rightarrow \infty}\left(x+1-\sqrt{a x^{2}+x+3}\right) \) exists finitely, then...

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If \( L=\lim _{x \rightarrow \infty}\left(x+1-\sqrt{a x^{2}+x+3}\right) \) exists finitely, then the value of \( L \) is
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