Question

Calcule o limite dado abaixo:
lim ( 3x4 + 2x2 – x + 1)
x→ - 2

a.
42
b.
52
c.
59
d.
36
e.
48

Answer 1

Resposta:

c

Explicação passo-a-passo:

3.(-2)⁴+2.(-2)²-(-2)+1

3.16+2.4+2+1

48+8+3

59

Answer 2

Resposta:

$\sf L=\underset{x\to-2}{lim}(3x^4+2x^2-x+1)$

$\sf L=\underset{x\to-2}{lim}3x^4+\underset{x\to-2}{lim}2x^2-\underset{x\to-2}{lim}x+\underset{x\to-2}{lim}1$

$\sf L=3\cdot\underset{x\to-2}{lim}x^4+2\cdot\underset{x\to-2}{lim}x^2-\underset{x\to-2}{lim}x+\underset{x\to-2}{lim}1$

$\sf L=3\cdot\big(\underset{x\to-2}{lim}x\big)^4+2\cdot\big(\underset{x\to-2}{lim}x\big)^2-\underset{x\to-2}{lim}x+\underset{x\to-2}{lim}1$

$\sf L=3\cdot(-2)^4+2\cdot(-2)^2-(-2)+1$

$\sf L=3\cdot16+2\cdot4+2+1$

$\sf L=48+8+2+1$

$\red{\sf L=59}$

O limite existe e é igual a 59.

Letra C

Propriedades usadas:

• $\sf \underset{x\to a}{lim}(f(x)\pm g(x))=\underset{x\to a}{lim}(f(x))\pm\underset{x\to a}{lim}(g(x))$

• $\sf \underset{x\to a}{lim}(c\cdot f(x))=c\cdot\underset{x\to a}{lim}(f(x))$

• $\sf \underset{x\to a}{lim}((f(x))^n)=\big[\underset{x\to a}{lim}(f(x))\big]^n,~n\neq1$

• $\sf \underset{x\to a}{lim}(c)=c$

• $\sf \underset{x\to a}{lim}(x)=a$