Question

lim (x2-6x+9)/(x-3) quando x tende a 3 ?

Answer 1

$\lim\limits_{x\rightarrow3}~\dfrac{x^{2}-6x+9}{x-3}=\lim\limits_{x\rightarrow3}~\dfrac{x^{2}-2\cdot3\cdot x+3^{2}}{x-3}\\\\\\\lim\limits_{x\rightarrow3}~\dfrac{x^{2}-6x+9}{x-3}=\lim\limits_{x\rightarrow3}~\dfrac{(x-3)^{2}}{x-3}\\\\\\\lim\limits_{x\rightarrow3}~\dfrac{x^{2}-6x+9}{x-3}=\lim\limits_{x\rightarrow3}~x-3\\\\\\\lim\limits_{x\rightarrow3}~\dfrac{x^{2}-6x+9}{x-3}=3-3\\\\\\\boxed{\boxed{\lim\limits_{x\rightarrow3}~\dfrac{x^{2}-6x+9}{x-3}=0}}$

Answer 2

Resposta:

Explicação passo-a-passo:

lim (x2-6x+9)/(x-3) x>3

(x+3) . (x-3)/(x-3)

x+3

=6