Question

Calcule o Limite:
$\lim_{x \to 2}\frac{3x^2-4x-4}{x-2}$

Answer 1

Resolução da questão, veja:

Vamos reescrever esse limite pela diferença entre dois produtos, veja:

$\mathtt{\displaystyle\lim_{x~\to~2}\dfrac{3x^{2}-4x-4}{x-2}}} =\mathtt{\displaystyle\lim_{x~\to~2}\dfrac{(x-2)~\cdot~(3x+2)}{(x-2)}}}}}}}}~\textsf{Cortando~os~termos~semelhantes~(x~-~2),~teremos~o~novo~limite}:}}}}}\\\\\\\\\\ \mathtt{\displaystyle\lim_{x~\to~2}~3x+2}}}}}}}}\\\\\\\\ \mathtt{\displaystyle\lim_{x~\to~2}=3~\cdot~2+2}}}\\\\\\\\\ \mathtt{\displaystyle\lim_{x~\to~2}=6+2}}}}}}}\\\\\\\\\\ \Large\boxed{\boxed{\boxed{\boxed{\mathbf{\displaystyle\lim_{x~\to~2}\dfrac{3x^{2}-4x-4}{x-2}=8.}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

Espero que te ajude. '-'