lim-x-x-2-cot-1-x-4cot-1-x-3x-2-2x-

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Question Number 131156 by EDWIN88 last updated on 02/Feb/21

$$\underset{x\to \mathrm{\infty }}{\lim }\frac{x^2\cot \left(\frac{1}{x}\right)+4\cot \left(\frac{1}{x}\right)}{3x^2+2x}?$$

Answered by john_santu last updated on 02/Feb/21

$$\underset{x\to \mathrm{\infty }}{\lim }\frac{x^2+4}{x(3x+2).\tan \left(\frac{1}{x}\right)}=$$$$\underset{x\to \mathrm{\infty }}{\lim }\frac{x^2+4}{3x+2}=\underset{x\to \mathrm{\infty }}{\lim }\frac{1+\frac{4}{x^2}}{\frac{3}{x}+\frac{2}{x^2}}=\mathrm{\infty }$$

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