?Find the limit or show that it does not exist.\(\lim \limits_{x \rightarrow

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The given limit is \(\lim \limits_{x \rightarrow \infty}\left(\sqrt{x^{2}+a x}-\sqrt{x^{2}+b x}\right)\).

Let us evaluate the value of \(\lim \limits_{x \rightarrow \infty}\left(\sqrt{x^{2}+a x}-\sqrt{x^{2}+b x}\right)\):

\(\begin{aligned} \lim _{x \rightarrow \infty}\left(\sqrt{x^{2}+a x}-\sqrt{x^{2}+b x}\right) & =\sqrt{\infty^{2}+a(\infty)}-\sqrt{\infty^{2}+b(\infty)} \\ & =\text { indeterminate form } \end{aligned}\)