Ltx→∞ x2+5x+73x3+5x2+8=

Ltx→∞ x21+5x+7x2x33+5x+8x3=Ltx→∞ 1x 1+5x+7x23+5x+8x3=Lt1x→0 1x1+5x+7x23+5x+8x3=0

Ltx→∞ x21+5x+7x2x33+5x+8x3=Ltx→∞ 1x 1+5x+7x23+5x+8x3=Lt1x→0 1x1+5x+7x23+5x+8x3=0

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$\underset{x \to \infty}{L t} \frac{x^{2} + 5 x + 7}{3 x^{3} + 5 x^{2} + 8} =$

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$\underset{x \to \infty}{L t} \frac{x^{2} (1 + \frac{5}{x} + \frac{7}{x^{2}})}{x^{3} (3 + \frac{5}{x} + \frac{8}{x^{3}})}$

$= \underset{x \to \infty}{L t} \frac{1}{x} (\frac{1 + \frac{5}{x} + \frac{7}{x^{2}}}{3 + \frac{5}{x} + \frac{8}{x^{3}}})$

$= \underset{\frac{1}{x} \to 0}{L t} (\frac{1}{x} (\frac{1 + \frac{5}{x} + \frac{7}{x^{2}}}{3 + \frac{5}{x} + \frac{8}{x^{3}}})) = 0$

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