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\lim_{x \to \infty} (\sqrt{ax^2 + bx + c} - \sqrt{ax^2 + px + q}) = \frac{b - p}{2 \sqrt{a}}

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???

Here is what I get

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\lim_{x \to \infty} (\sqrt{ax^2 + bx + c} - \sqrt{ax^2 + px + q})

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= \sqrt{\lim_{x \to \infty} ax^2 + \lim_{x \to \infty} bx + \lim_{x \to \infty} c} - \sqrt{\lim_{x \to \infty} ax^2 + \lim_{x \to \infty} px + \lim_{x \to \infty} q}

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=\sqrt{\infty + \infty + c} - \sqrt{\infty + \infty + q}

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= \sqrt{\infty} - \sqrt{\infty}

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= \infty

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# How to Find This Limit?

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