Question

Assinale a alternativa que indica o valor do limite
lim x-> -1 (3x²+2x-1/-x²+3x+4)²
Alternativas:
(A) - 16/25
(B) - 36/25
(C) - 1/16
(D - 1/25
(E) - 1/4

Answer 1

ax²+bx+c=a*(x-x')*(x-x'')

3x²+2x -1=0 ==>x'=-1   e  x''= 1/3

3x²+2x -1=3*(x+1)*(x-1/3) =(x+1)*(3x-1)

-x²+3x+4 = 0 ==>x'=-1   e  x''= 4

-x²+3x+4 = -1*(x+1)*(x-4) =(x+1)*(4-x)

Lim (3x²+2x -1)/(-x²+3x+4)

x-->-1

Lim (x+1)*(3x-1)/(x+1)*(4-x)

x-->-1

Lim  (3x-1)/(4-x)   =(-3-1)/(4+1) =(-4/5)² = 16/25

RESPOSTA= ALTERNATIVA "A"

x-->-1