Question

Calcule o seguinte limite: $\lim_{x \to \ 2}(\frac{x^2-x-2}{x^2-5x+6} )$

Answer 1

Resposta:

ax²+bx+c=a*(x-x')*(x-x'')     .....a≠0    e x'  e x'' são as raízes

x²-x-2=0  ==>x'=-1  e x''=2  ...a=1

x²-x-2=(x+1)*(x-2)

x²-5x+6=0  ==>x'=2  e x''=3  ...a=1

x²-5x+6=(x-3)*(x-2)

lim (x+1)*(x-2)/[(x-3)*(x-2)]

x-->2

lim (x+1)/(x-3)  = (2+1)/(2-3) = -3

x-->2