Question

Considere a função:

$f(x)= \frac{ x^{2} -5x+6}{x-2}$

Qual é o valor de $\lim_{x \to 2} f(x)$ ?

Answer 1

$\underset{x\to 2}{\mathrm{\ell im}}~\dfrac{x^2-5x+6}{x-2}\\\\\\ =\underset{x\to 2}{\mathrm{\ell im}}~\dfrac{x^2-2x+2x-5x+6}{x-2}\\\\\\ =\underset{x\to 2}{\mathrm{\ell im}}~\dfrac{x^2-2x-3x+6}{x-2}\\\\\\ =\underset{x\to 2}{\mathrm{\ell im}}~\dfrac{x\cdot (x-2)-3\cdot(x-2)}{x-2}\\\\\\ =\underset{x\to 2}{\mathrm{\ell im}}~\dfrac{(x-2)(x-3)}{x-2}\\\\\\ =\underset{x\to 2}{\mathrm{\ell im}}~(x-3)\\\\ =2-3\\\\ =-1\\\\\\ \therefore~~\boxed{\begin{array}{c} \underset{x\to 2}{\mathrm{\ell im}}~\dfrac{x^2-5x+6}{x-2}=-1 \end{array}}$


Bons estudos! :-)