Resposta:
lim [3-x³]⁴-16/(x³-1)
x-->1
lim {[3-x³]²-4}{[3-x³]²+4}/(x³-1)
x-->1
lim {[3-x³]-2}{[3-x³]+2}{[3-x³]²+4}/(x³-1)
x-->1
lim {1-x³}{[3-x³]+2}{[3-x³]²+4}/(x³-1)
x-->1
lim -{x³-1}{[3-x³]+2}{[3-x³]²+4}/(x³-1)
x-->1
lim -{[3-x³]+2}{[3-x³]²+4}
x-->1
=-{[3-1³]+2}{[3-1³]²+4}
=-{2+2}*{4+4}
Olá, siga a explicação:
[tex]\mathrm {\displaystyle \lim_{x \to 1} \left ( \dfrac{ \left ( 3-x^3 \right ) ^4 - 16 }{x^3 -1} \right ) }[/tex]
Expandi:
[tex]\mathrm { \dfrac{ \left ( 3-x^3 \right )^4 -16 }{x^3 -1} : ~ \dfrac{x^{11} + x^{10} + x^9 - 11x^8 - 11x^7 - 11x^6 + 43x^5 + 43x^4 + 43x^3- 65x^2 - 65x - 65}{x^2 + x +1} }[/tex][tex]\mathrm { \displaystyle \lim_{x \to 1} \left ( \dfrac{x^{11} + x^{10} + x^9- 11x^8-11x^7-11x^6+43x^5+43x^4+43x^3-65x^2-65x -65}{x^2+x+1} \right ) }[/tex][tex]\mathrm { \dfrac{1^{11} + 1^{10} + 1^9 -11 \cdot 1^8 -11 \cdot 1^7 -11 \cdot 1^6 + 43 \cdot 1^5 + 43 \cdot 1^4 + 43 \cdot 1^3 - 65 \cdot 1^2 - 65 \cdot 1 - 65}{1^2+ 1 +1 } }[/tex]Simplifica:
[tex]\mathrm { \dfrac{1^{11} + 1^{10} + 1^9 -11 \cdot 1^8 -11 \cdot 1^7 -11 \cdot 1^6 + 43 \cdot 1^5 + 43 \cdot 1^4 + 43 \cdot 1^3 - 65 \cdot 1^2 - 65 \cdot 1 - 65}{3} }[/tex]∴ [tex] \boxed { \sf -32} [/tex]
⇒ Bons Estudos! シ
