Question

Limite x2 + 5x + 6/ x +2 quando x tende a 2

Answer 1

Lim (x²+5x+6)/(x+2)
x-->2

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

x²+5x+6=0
x'=[-5+√(25-24)]/2 =[-5+1]/2=-2
x''=[-5-√(25-24)]/2 =[-5-1]/2=-3
x²+5x+6=(x+2)(x+3)


Lim (x²+5x+6)/(x+2)
x-->2

Lim (x+2)(x+3)/(x+2)
x-->2

Lim  (x+3)   =2+3=5
x-->2