Question

Se lim x= -1 então......

133ae009b972d648ef092aaa9abc161b.pdf

Answer 1

$\lim\limits_{x\rightarrow-1}~3^{(x^{3}+3x+2)}=\lim\limits_{x\rightarrow-1}~(3^{x^{3}}\cdot3^{3x}\cdot3^{2})$

Sabe-se que funções exponenciais são contínuas em todo seu domínio, portanto os limites existem e são iguais a f(-1).

$\lim\limits_{x\rightarrow-1}~3^{(x^{3}+3x+2)}=\lim\limits_{x\rightarrow-1}~3^{x^{3}}\cdot\lim\limits_{x\rightarrow-1}~3^{3x}\cdot\lim\limits_{x\rightarrow-1}~3^{2}\\\\\\\lim\limits_{x\rightarrow-1}~3^{(x^{3}+3x+2)}=3^{(-1)^{3}}\cdot3^{3(-1)}\cdot3^{2}\\\\\\\lim\limits_{x\rightarrow-1}~3^{(x^{3}+3x+2)}=3^{-1}\cdot3^{-3}\cdot3^{2}\\\\\\\lim\limits_{x\rightarrow-1}~3^{(x^{3}+3x+2)}=3^{-1-3+2}\\\\\\\lim\limits_{x\rightarrow-1}~3^{(x^{3}+3x+2)}=3^{-2}=\dfrac{1}{3^{2}}$

Portanto:

$\boxed{\boxed{\lim\limits_{x\rightarrow-1}~3^{(x^{3}+3x+2)}=\dfrac{1}{9}}}$

Answer 2

$\lim_{x \to \ -1} 3^{ x^{3} +3x+2} \\ 3^{-1-3+2}=3^{-2}$
=1/9