Question

Identifique o valor de $\lim_{x \to \infty} (\frac{3x-4}{-x+4} )$.
Escolha uma:
a. 3
b. - 3
c. - ∞
d. 0
e. + ∞

Answer 1

Resposta:

b. -3

Explicação passo-a-passo:

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

$\frac{3-0}{-1+0} =\frac{3}{-1} =-3$

Answer 2

$\mathtt{\lim_{x \to~+\infty}\dfrac{3x-4}{-x+4}} \\ \mathtt{\lim_{x \to~+\infty}\dfrac{ \cancel{x}(3 - \frac{4}{x})}{ \cancel{x}(-1+ \frac{4}{x}) }}$

$\mathtt{\lim_{x \to~+\infty}\dfrac{3-\frac{4}{x}}{-1+\frac{4}{x}}=-3}$