Question

Que se habilita a responder essa questão de cálculo 1?

Answer 1

Resposta:

Lim [√(4x-3) -3]/(x³-2x²-9)

x-->3

Lim [√(4x-3) -3][√(4x-3) +3]/[(x³-2x²-9)[√(4x-3) +3]]

x-->3

Lim [4x-3 -9]/[(x³-2x²-9)[√(4x-3) +3]

x-->3

Lim [4x-12]/[(x³-2x²-9)[√(4x-3) +3]]

x-->3

Lim 4*[x-3]/[(x³-2x²-9)[√(4x-3) +3]]

x-->3

**************************************************************

3  é raiz de x³-2x²-9

diminuindo um grau , utilizando Ruffini

    |     1    |    -2   |    0    |   -9

3   |     1    |   1     |     3    |   0

x³-2x²-9 =(x-3)* (x²+x+3)

************************************************************

Lim 4*[x-3]/[(x-3)* (x²+x+3)[√(4x-3) +3]]

x-->3

Lim 4/ [(x²+x+3)[√(4x-3) +3]]  =4/[(9+3+3)*(3+3) =4/90=2/45

x-->3