[latex]mathrm{ lim_{n o infty} frac{3n^7+8n-11}{n+8} = lim_{n o infty} frac{3n^6+8- frac{11}{n} }{1+ frac{8}{n} } = infty} \ \ \ mathrm{lim_{n o infty} frac{ sqrt{n^2+3n} }{4n-2} = lim_{n o infty} frac{ sqrt{1+ frac{3}{n}} }{4- frac{2}{n}} = frac{1}{4}}[/latex]
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