Question

lim ³√x- ³√3/x-3 , x tende a 3​

Answer 1

lim  [∛x -∛3]/(x-3)

x-->3

(a-b)³=a³-3a²b+3ab²-b³

(a-b)³=a³-b³-3ab(a-b)

a³-b³=(a-b)*[(a-b)²+3ab]

a³-b³=(a-b)*(a²+ab+b²)

Fazendo a=∛x  e b=∛3

∛x-∛3  =(x-3)/(∛x²+∛x*∛3+∛3²)

lim  (x-3)/[(∛x²+∛x*∛3+∛3²)*(x-3)]

x-->3

lim  1/(∛x²+∛x*∛3+∛3²)

x-->3

=1/(∛9+∛9+∛9)=1/3∛9  é a resposta

ou ∛3/9