Question

Докажите, что:
1) $lim_{x to+ infty} frac{2x+5}{3x} = frac{2}{3}$
2) $lim_{x to +infty} frac{3 x^{2} + 6}{ x^{2} } = 3$
3) $lim_{x to +infty} frac{5x+14}{x+2} = 5$

Answer 1

$lim_{n to +infty} frac{2x+5}{3x}= lim_{n to infty} frac{frac{2x}x+frac{5}x}{frac{3x}x}= lim_{n to infty} frac{2+frac{5}x}{3}=frac{2}3\\ lim_{n to +infty} frac{3x^2+6}{x^2}=lim_{n to +infty} frac{frac{3x^2}{x^2}+frac{6}{x^2}}{frac{x^2}{x^2}}=lim_{n to +infty} frac{3+frac{6}{x^2}}{1}=3\\ lim_{n to +infty} frac{5x+14}{x+2}=lim_{n to +infty} frac{frac{5x}x+frac{14}x}{frac{x}x+frac{x}2}=lim_{n to +infty} frac{5+frac{14}x}{1+frac{2}x}=5$

Answer 2

Спасибо !!