Question

Lim(x->2+)(x²-4 )/ (x-2)

Answer 1

$\lim\limits_{x\rightarrow2}\dfrac{x^{2}-4}{x-2}=\lim\limits_{x\rightarrow2}\dfrac{x^{2}-2^{2}}{x-2}$

x² - 2² é o resultado de um produto notável:

$a^{2}-b^{2}=(a+b)(a-b)$

Substituindo:

$\lim\limits_{x\rightarrow2}\dfrac{x^{2}-4}{x-2}=\lim\limits_{x\rightarrow2}\dfrac{(x+2)(x-2)}{x-2}\\\\\\\lim\limits_{x\rightarrow2}\dfrac{x^{2}-4}{x-2}=\lim\limits_{x\rightarrow2}x+2\\\\\\\lim\limits_{x\rightarrow2}\dfrac{x^{2}-4}{x-2}=2+2\\\\\\\boxed{\boxed{\lim\limits_{x\rightarrow2}\dfrac{x^{2}-4}{x-2}=4}}$