Question

o limite da funcaof (x)= ( x elevado a cubo menos 3) sobre x quando x tende a 0 e?

Answer 1

É indeterminado para x = 0. Para os limites laterais:

$\lim_{x \to 0} \frac{x^3 - 3}{x} =\\\\ \lim_{x \to 0} (\frac{x^3}{x} - \frac{3}{x})=\\\\ \lim_{x \to 0} (x^2 - \frac{3}{x})=\\\\ \lim_{x \to 0} x^2 - \lim_{x \to 0}\frac{3}{x}=\\\\ 0 + \lim_{x \to 0}-\frac{3}{x}=\\\\ \lim_{x \to 0}-\frac{3}{x}=\\\\ \lim_{x \to 0}(-3 \times \frac{1}{x})=\\\\ \lim_{x \to 0}-3 \times \lim_{x \to 0}\frac{1}{x}=\\\\ -3 \times \lim_{x \to 0}\frac{1}{x}=\\\\ \begin{cases} -3\time\lim_{x \to 0^+} = -\infty\\ -3\time\lim_{x \to 0^-} = +\infty \end{cases}$