Question

lim x^3 - 1/ x^2 - 1 quando x tende a 1?​

Answer 1

Resposta:

Lim (x³-1)/(x²-1)

x-->1

(x-1)³=x³-3x²+3x-1

(x-1)³=x³-1-3x*(x-1)

x³-1=(x-1)³+3x*(x-1)

x³-1=(x-1)*[(x-1)²+3x]

x³-1=(x-1)*(x²-2x+1+3x)

x³-1=(x-1)*(x²+x+1)

x²-1=(x-1)*(x+1)

Lim  (x-1)*(x²+x+1)/(x-1)*(x+1)

x-->1

Lim  (x²+x+1)/(x+1)  = (1+1+1)/(1+1)=3/2

x-->1