Question

O limite x2 - 9 / x2 - 5 x + 6 é: x → 3

Answer 1

Resolução da questão, veja:

Esse limite pode ser reescrito de modo conveniente, veja:

Desmembrando a função em partes:

$\mathsf{\displaystyle\lim_{x~\to~3}~\dfrac{x^{2}-9}{x^{2}-5x+6}}}}\\\\\\\\\ \mathsf{\displaystyle\lim_{x~\to~3}\dfrac{(x-3)~\cdot~(x+3)}{(x-3)~\cdot~(x-2)}}}}}~~\textsf{Cortando~os~semelhantes~((x-3)),~temos~o~novo~limite}:\\\\\\\\\\ \mathsf{\displaystyle\lim_{x~\to~3}\dfrac{(x+3)}{(x-2)}}}}}}}}}}~~\textsf{Substituindo~x~por~3,~teremos}}:\\\\\\\\\ \mathsf{\dfrac{3+3}{3-2}}}}}\\\\\\\\\ \mathsf{\dfrac{6}{1}}\\\\\\\\\\ \large\boxed{\boxed{\boxed{\boxed{\mathsf{\displaystyle\lim_{x~\to~3}~\dfrac{x^{2}-9}{x^{2}-5x+6}=6.}}}}}}}}}}}}}}}}}}}}}}$

Espero que te ajude. '-'