O valor do limite é
[tex]\Large\displaystyle\text{$\begin{gathered} \lim_{x \to -\sqrt{2} } \left(4x^3-2x^2-2x-1\right) =-6\sqrt{2} -5\end{gathered}$}[/tex]
Desejamos calcular o seguinte limite
[tex]\Large\displaystyle\text{$\begin{gathered} \lim_{x \to -\sqrt{2} } \left(4x^3-2x^2-2x-1\right) \end{gathered}$}[/tex]
De praxe devemos substituir o valor que o x tende na função dada, caso de uma indeterminação matemática, devemos manipular de alguma forma, logo
[tex]\Large\displaystyle\text{$\begin{gathered} \lim_{x \to -\sqrt{2} } \left(4x^3-2x^2-2x-1\right) \end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered}\left(4(-\sqrt{2} )^3-2(-\sqrt{2} )^2-2(-\sqrt{2} )-1\right) \end{gathered}$}[/tex] [tex]\Large\displaystyle\text{$\begin{gathered}\left(4(-\sqrt{2} )(-\sqrt{2} )(-\sqrt{2} )-2(-\sqrt{2} )(-\sqrt{2} )-2(-\sqrt{2} )-1\right) \end{gathered}$}[/tex]
Vale resaltar a seguinte propriedade de radiciação
[tex]\Large\displaystyle\text{$\begin{gathered} *\ \ \sqrt{a} \cdot \sqrt{a} = a \end{gathered}$}[/tex]
Temos então que
[tex]\Large\displaystyle\text{$\begin{gathered}\left(4(-\sqrt{2} )(-\sqrt{2} )(-\sqrt{2} )-2(-\sqrt{2} )(-\sqrt{2} )-2(-\sqrt{2} )-1\right) \end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered}\left(4(-2)(\sqrt{2} )-2(2)-2(-\sqrt{2} )-1\right) \end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered}\left(-8\sqrt{2} -4+2\sqrt{2} -1\right) \end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered}\therefore \boxed{ -6\sqrt{2} -5} \end{gathered}$}[/tex]
