Question

Помогите решить, пожалуйста

$lim_{x to infty} frac{7x+9}{6x-1}$
$lim_{x to infty} frac{-2x-1}{3 x^2-4x+1} }$
$lim_{x to infty} frac{10 x^{2}+4x-3 }{5 x^{2}+2x+1 }$
$lim_{x to -frac{1}{3} } frac{7x-14} {21x+2 }$

Answer 1

1)
$lim_{x to infty} frac{ frac{7x}{x}+ frac{9}{x} }{ frac{6x}{x}- frac{1}{x} }= lim_{x to infty} frac{7+ frac{9}{x} }{6- frac{1}{x} }= frac{7}{6}=1 frac{1}{6}$

2)
$lim_{x to infty} frac{- frac{2x}{x^2}- frac{1}{x^2} }{ frac{3x^2}{x^2}- frac{4x}{x^2}+ frac{1}{x^2} }= lim_{x to infty} frac{- frac{2}{x}- frac{1}{x^2} }{3- frac{4}{x}+ frac{1}{x^2} }= frac{0}{3}=0$

3)
$lim_{x to infty} frac{ frac{10x^2}{x^2}+ frac{4x}{x^2}- frac{3}{x^2} }{ frac{5x^2}{x^2}+ frac{2x}{x^2}+ frac{1}{x^2} }= lim_{x to infty} frac{10+ frac{4}{x}- frac{3}{x^2} }{5+ frac{2}{x}+ frac{1}{x^2} }= frac{10}{5}=2$

4)
$frac{7*(- frac{1}{3} )-14}{21*(- frac{1}{3} )+2}= frac{- frac{7}{3} - frac{42}{3} }{-7+2}=- frac{49}{3}* frac{1}{5}=- frac{49}{15}=-3 frac{4}{15}$