lim-s-20s-2-2s-5s-2-1-5s-2-2s-

Question Number 111383 by john santu last updated on 03/Sep/20

\lim_{s \to \infty} \sqrt{20 s^{2} + 2 s} - \sqrt{5 s^{2} + 1} - \sqrt{5 s^{2} - 2 s}

Answered by bobhans last updated on 03/Sep/20

L_{1} = \lim_{s \to \infty} \sqrt{{20 s}^{2} + 2 s} - \sqrt{{20 s}^{2}} = \frac{2 - 0}{2 \sqrt{20}} = \frac{1}{2 \sqrt{5}}

L_{2} = \lim_{s \to \infty} \sqrt{{5 s}^{2}} - \sqrt{{5 s}^{2} + 1} = 0

L_{3} = \lim_{s \to \infty} \sqrt{{5 s}^{2}} - \sqrt{{5 s}^{2} - 2 s} = \frac{0 - (- 2)}{2 \sqrt{5}} = \frac{1}{\sqrt{5}}

L = L_{1} + L_{2} + L_{3} = \frac{1}{2 \sqrt{5}} + \frac{1}{\sqrt{5}} = \frac{3}{2 \sqrt{5}} = \frac{3 \sqrt{5}}{10}

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