Докажите, что: 1) [latex] \lim_{x \to+ \infty} \frac{2x+5}{3x} = \frac{2}{3} [/latex] 2) [latex] \lim_{x \to +\infty} \frac{3 x^{2} + 6}{ x^{2} } = 3[/latex] 3) [latex] \lim_{x \to +\infty} \frac{5x+14}{x+2} = 5[/latex]

[latex] \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[/latex]