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![lim_{x to infty} frac{ frac{7x}{x}+ frac{9}{x} }{ frac{6x}{x}- frac{1}{x} }= lim_{x to infty} frac{7+ frac{9}{x} }{6- frac{1}{x} }= frac{7}{6}=1 frac{1}{6} lim_{x to infty} frac{ frac{7x}{x}+ frac{9}{x} }{ frac{6x}{x}- frac{1}{x} }= lim_{x to infty} frac{7+ frac{9}{x} }{6- frac{1}{x} }= frac{7}{6}=1 frac{1}{6}](https://tex.z-dn.net/?f=+lim_%7Bx+to+infty%7D++frac%7B+frac%7B7x%7D%7Bx%7D%2B+frac%7B9%7D%7Bx%7D++%7D%7B+frac%7B6x%7D%7Bx%7D-+frac%7B1%7D%7Bx%7D++%7D%3D+lim_%7Bx+to+infty%7D++frac%7B7%2B+frac%7B9%7D%7Bx%7D+%7D%7B6-+frac%7B1%7D%7Bx%7D+%7D%3D+frac%7B7%7D%7B6%7D%3D1+frac%7B1%7D%7B6%7D++++++)
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![lim_{x to infty} frac{- frac{2x}{x^2}- frac{1}{x^2} }{ frac{3x^2}{x^2}- frac{4x}{x^2}+ frac{1}{x^2} }= lim_{x to infty} frac{- frac{2}{x}- frac{1}{x^2} }{3- frac{4}{x}+ frac{1}{x^2} }= frac{0}{3}=0 lim_{x to infty} frac{- frac{2x}{x^2}- frac{1}{x^2} }{ frac{3x^2}{x^2}- frac{4x}{x^2}+ frac{1}{x^2} }= lim_{x to infty} frac{- frac{2}{x}- frac{1}{x^2} }{3- frac{4}{x}+ frac{1}{x^2} }= frac{0}{3}=0](https://tex.z-dn.net/?f=+lim_%7Bx+to+infty%7D+frac%7B-+frac%7B2x%7D%7Bx%5E2%7D-+frac%7B1%7D%7Bx%5E2%7D++%7D%7B+frac%7B3x%5E2%7D%7Bx%5E2%7D-+frac%7B4x%7D%7Bx%5E2%7D%2B+frac%7B1%7D%7Bx%5E2%7D+++%7D%3D+lim_%7Bx+to+infty%7D++frac%7B-+frac%7B2%7D%7Bx%7D-+frac%7B1%7D%7Bx%5E2%7D++%7D%7B3-+frac%7B4%7D%7Bx%7D%2B+frac%7B1%7D%7Bx%5E2%7D++%7D%3D+frac%7B0%7D%7B3%7D%3D0+++++)
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![lim_{x to infty} frac{ frac{10x^2}{x^2}+ frac{4x}{x^2}- frac{3}{x^2} }{ frac{5x^2}{x^2}+ frac{2x}{x^2}+ frac{1}{x^2} }= lim_{x to infty} frac{10+ frac{4}{x}- frac{3}{x^2} }{5+ frac{2}{x}+ frac{1}{x^2} }= frac{10}{5}=2 lim_{x to infty} frac{ frac{10x^2}{x^2}+ frac{4x}{x^2}- frac{3}{x^2} }{ frac{5x^2}{x^2}+ frac{2x}{x^2}+ frac{1}{x^2} }= lim_{x to infty} frac{10+ frac{4}{x}- frac{3}{x^2} }{5+ frac{2}{x}+ frac{1}{x^2} }= frac{10}{5}=2](https://tex.z-dn.net/?f=+lim_%7Bx+to+infty%7D++frac%7B+frac%7B10x%5E2%7D%7Bx%5E2%7D%2B+frac%7B4x%7D%7Bx%5E2%7D-+frac%7B3%7D%7Bx%5E2%7D+++%7D%7B+frac%7B5x%5E2%7D%7Bx%5E2%7D%2B+frac%7B2x%7D%7Bx%5E2%7D%2B+frac%7B1%7D%7Bx%5E2%7D+++%7D%3D+lim_%7Bx+to+infty%7D++frac%7B10%2B+frac%7B4%7D%7Bx%7D-+frac%7B3%7D%7Bx%5E2%7D++%7D%7B5%2B+frac%7B2%7D%7Bx%7D%2B+frac%7B1%7D%7Bx%5E2%7D++%7D%3D+frac%7B10%7D%7B5%7D%3D2+++++)
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![frac{7*(- frac{1}{3} )-14}{21*(- frac{1}{3} )+2}= frac{- frac{7}{3} - frac{42}{3} }{-7+2}=- frac{49}{3}* frac{1}{5}=- frac{49}{15}=-3 frac{4}{15} frac{7*(- frac{1}{3} )-14}{21*(- frac{1}{3} )+2}= frac{- frac{7}{3} - frac{42}{3} }{-7+2}=- frac{49}{3}* frac{1}{5}=- frac{49}{15}=-3 frac{4}{15}](https://tex.z-dn.net/?f=+frac%7B7%2A%28-+frac%7B1%7D%7B3%7D+%29-14%7D%7B21%2A%28-+frac%7B1%7D%7B3%7D+%29%2B2%7D%3D+frac%7B-+frac%7B7%7D%7B3%7D+-+frac%7B42%7D%7B3%7D+%7D%7B-7%2B2%7D%3D-+frac%7B49%7D%7B3%7D%2A+frac%7B1%7D%7B5%7D%3D-+frac%7B49%7D%7B15%7D%3D-3+frac%7B4%7D%7B15%7D+++++)
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