lim-x-2x-cot-2-x-3cot-2-x-5x-2-2x-

Question Number 114088 by bemath last updated on 17/Sep/20

\lim_{x \to \infty} \frac{2 x \cot (\frac{2}{x}) - 3 \cot (\frac{2}{x})}{5 x^{2} - 2 x}

Answered by Olaf last updated on 17/Sep/20

= \lim_{x \to \infty} \frac{1 - \frac{1}{2} {(\frac{2}{x})}^{2}}{(\frac{2}{x})} [\frac{2 x - 3}{5 x^{2} - 2 x}]

= \lim_{x \to \infty} \frac{x^{2} - 2}{2 x} \times \frac{2 x - 3}{5 x^{2} - 2 x}

= \lim_{x \to \infty} \frac{2 x^{3}}{10 x^{3}} = \frac{1}{5}

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