Мат анализ хелп я студентРешите два примера

1. $\lim_{x \to \infty} \frac{4x+1}{x+2}; \lim_{x \to \infty} 4x+1; \lim_{x \to \infty} x+2; +00; +00; \lim_{x \to \infty} \frac{4x+1}{x+2} = \lim_{x \to \infty} \frac{x*(4+1/x)}{x*(1+2/x)}= \lim_{x \to \infty} \frac{4+1/x}{1+2/x};\frac{4+0}{1+0};4$

2. $\lim_{x \to \infty} x-\sqrt{x*(x-1)} ;\lim_{x \to \infty} x} ;\lim_{x \to \infty} \sqrt{x*(x-1)} ;$ +00; +00; $\lim_{x \to \infty} x-\sqrt{x*(x-1)}=\lim_{x \to \infty} (x-\sqrt{x*(x-1)}*\frac{x+\sqrt{x*(x-1)} }{x+\sqrt{x*(x-1)} }$ = $\lim_{x \to \infty} \frac{(x-\sqrt{x(x-1)}) *(x+\sqrt{x*(x-1)}}{x+\sqrt{x*(x-1) }}$ = $\lim_{x \to \infty} \frac{x^{2}-x*(x-1) }{x+\sqrt{x^{2}-x}}$ = $\lim_{x \to \infty} \frac{x^{2}-x^{2} + x}{x+\sqrt{x^{2} -x}}$ = $\lim_{x \to \infty} \frac{x }{x+\sqrt{x^{2} -x}}$

$\lim_{x \to \infty} \frac{x}{x* (1+\sqrt{1-1/x}}$ = $\frac{1}{1+\sqrt{1-0} } =\frac{1}{2}$