- #1
askor
- 169
- 9
How to find the
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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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\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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