Question

Calcule os valor do limite expressos abaixo:

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Answer 1

Temos que

$\: \: \: \: \: \displaystyle\lim_{x\rightarrow \infty} \frac{4 {x}^{2} + x + 3}{3 {x}^{3} + 5{x}^{2} + x + 2} \\ = \displaystyle\lim_{x\rightarrow \infty} \frac{ {x}^{3}( \frac{4}{x} + \frac{1}{ {x}^{2} } + \frac{3}{ {x}^{3} }) }{{x}^{3}(3 + \frac{5}{x} + \frac{1}{ {x}^{2} } + \frac{2}{ {x}^{3} } )} \\ = \displaystyle\lim_{x\rightarrow \infty} \frac{ ( \frac{4}{x} + \frac{1}{ {x}^{2} } + \frac{3}{ {x}^{3} }) }{(3 + \frac{5}{x} + \frac{1}{ {x}^{2} } + \frac{2}{ {x}^{3} } )} \\ = \frac{(0 + 0 + 0)}{(3 + 0 + 0 + 0)} = \frac{0}{3} = 0$