Question

alguém que entende de limite ​

Answer 1

Resposta:

$\sf \lim_{x \to \dfrac{1}{2} } \bigg(\dfrac{2x - 1}{4x^{2} - 1} \bigg) = \dfrac{1}{2}$

Resolução:

$\sf \lim_{x \to \dfrac{1}{2} } \bigg(\dfrac{2x - 1}{4x^{2} - 1} \bigg)$

$\sf \lim_{x \to \dfrac{1}{2} } \bigg(\dfrac{2x - 1}{(2x - 1) \cdot (2x + 1)} \bigg) \quad \gets \mbox { Cancela (2x - 1) .}$

$\sf \lim_{x \to \dfrac{1}{2} } \bigg(\dfrac{1}{2x+ 1} \bigg) \quad \gets \mbox{aplicar o limite. }$

$\sf \lim_{x \to \dfrac{1}{2} } \Bigg(\dfrac{1}{2 \cdot \dfrac{1}{ 2} + 1} \Bigg)$

$\sf \lim_{x \to \dfrac{1}{2} } \bigg(\dfrac{1}{1 + 1} \bigg)$

$\sf \lim_{x \to \dfrac{1}{2} }\dfrac{1}{2}$