Question

limite de x³ - 4x² - 4 quando x tende ao infinito

Answer 1

Temos o seguinte:

$\lim_{x \to \infty} x^3 - 4x^2 - 4 = \lim_{x \to \infty} x^3(1 - \frac{4}{x} - \frac{4}{x^3} )$

Logo:

$\lim_{x \to \infty} \frac{4}{x} = 0 \\ \\ \lim_{x \to \infty} \frac{4}{x^3} = 0$

Assim:

$\lim_{x \to \infty} x^3(1 - 0 - 0 ) = \lim_{x \to \infty} x^3 = \infty^3 = \infty$

Answer 2

Resposta:

\lim_{x \to \infty} x^3 - 4x^2 - 4 = \lim_{x \to \infty} x^3(1 - \frac{4}{x} - \frac{4}{x^3} )lim

x→∞

x

3

−4x

2

−4=lim

x→∞

x

3

(1−

x

4

−

x

3

4

)

Logo:

\begin{gathered} \lim_{x \to \infty} \frac{4}{x} = 0 \\ \\ \lim_{x \to \infty} \frac{4}{x^3} = 0\end{gathered}

x→∞

lim

x

4

=0

x→∞

lim

x

3

4

=0

Assim:

\lim_{x \to \infty} x^3(1 - 0 - 0 ) = \lim_{x \to \infty} x^3 = \infty^3 = \inftylim

x→∞

x

3

(1−0−0)=lim

x→∞

x

3

=∞

3

=∞

espero ter ajudado.