Question

Va rog sa ma ajutati. Am incercat si formule de calcul prescurtat si favtor comun dar ceva imi scapa.
Lim x tinde la 3. X la 2-3x supra x la 2 - 7x +12

Answer 1

 

[tex]\displaystyle\\\lim_{x \to 3} \frac{x^2-3x}{x^2-7x+12} ~~~~~\text{Suntem in cazul: }~\frac{0}{0} \\\\ \text{Descompunem numaratorul si numitorul.}\\\\ x^2-3x = x(x-3)\\\\ x^2-7x+12=x^2-3x-4x+12=x(x-3)-4(x-3)=(x-3)(x-4)\\\\ \lim_{x \to 3} \frac{x^2-3x}{x^2-7x+12}=\lim_{x \to 3} \frac{x(x-3)}{(x-3)(x-4)}= \lim_{x \to 3} \frac{x}{(x-4)}=\frac{3}{(3-4)}=\boxed{\bf -3}[/tex]