Question

Calcule o limite de (está na foto)​

Answer 1

Resposta:

###∛x² -2∛x+1 =(∛x -1)²  <<<<<<<<<<

(a-1)³=a³-3a²+3a-1

(a-1)³=a³-1-3a*(a-1)

a³-1=(a-1)³+3a*(a-1)

a³-1=(a-1)*[(a-1)²+3a]

a³-1=(a-1)*[a²-2a+1+3a]

a³-1=(a-1)*[a²+a+1]

Fazendo  a =∛x

∛x³-1 =(∛x-1)*[∛x²+∛x+1]

x-1 =(∛x-1)*[∛x²+∛x+1] <<<<<<<<<<<<<

###############################

Lim   [∛x² -2∛x+1]/(x-1)²

x-->1

Lim   [(∛x -1)²]/[(∛x-1)*[∛x²+∛x+1]]²

x-->1

Lim   1/[[∛x²+∛x+1]]²  =1/(1+1+1)²=1/3²  =1/9

x-->1

Resposta  ==>  1/9