Lim x -> 3/2 Raiz de 8x^3 - 27 / 4x^2 - 9
Lim x -> 3/2V( 8x^3 - 27) / (4x^2 - 9))
(2x)^3-3^3=
(a^3 + b^3)=(a+b)*[a^2 + b^2- ab]=
(2x+3)(4x²+3²-2.3.x)
(2x)²-3²=(2x-3)(2x+3)
Lim x -> 3/2V( (2x+3)(4x²+3²-2.3.x)) / (2x-3)(2x+3))) ..... simplificando
Lim x -> 3/2V((4x²+9-6.x)) /(2x+3)))= V(9/4-6.3/2+9)/(2.3/2+3)=
V(9/4-9+9)/(6)=
3/2/V6=
3V6/12=
V6/4
/////////////////////////////////////////
a resposta abaixo esta errada pois nao eh (a^3 + b^3)=(a+b)*[a^2 + b^2- ab] e sim (a^3 - b^3)=(a-b)*[a^2 + b^2+ ab]
resumindo A^3 - B^3 (SUBTRAINDO)
Comments
Lim x -> 3/2V( 8x^3 - 27) / (4x^2 - 9))
(2x)^3-3^3=
(a^3 + b^3)=(a+b)*[a^2 + b^2- ab]=
(2x+3)(4x²+3²-2.3.x)
(2x)²-3²=(2x-3)(2x+3)
Lim x -> 3/2V( (2x+3)(4x²+3²-2.3.x)) / (2x-3)(2x+3))) ..... simplificando
Lim x -> 3/2V((4x²+9-6.x)) /(2x+3)))= V(9/4-6.3/2+9)/(2.3/2+3)=
V(9/4-9+9)/(6)=
3/2/V6=
3V6/12=
V6/4
/////////////////////////////////////////
a resposta abaixo esta errada pois nao eh (a^3 + b^3)=(a+b)*[a^2 + b^2- ab] e sim (a^3 - b^3)=(a-b)*[a^2 + b^2+ ab]
resumindo A^3 - B^3 (SUBTRAINDO)