Question

lim(3- 7x- 5x ²)
x → 0

Answer 1

Resposta:

Basta aplicar as propriedades:

$\sf L=\underset{x\to0}{lim}\,(3-7x-5x^2)$

$\sf L=\underset{x\to0}{lim}\,(3)-\underset{x\to0}{lim}\,(7x)-\underset{x\to0}{lim}\,(5x^2)$

$\sf L=\underset{x\to0}{lim}\,(3)-7\cdot\underset{x\to0}{lim}\,(x)-5\cdot\underset{x\to0}{lim}\,(x^2)$

$\sf L=\underset{x\to0}{lim}\,(3)-7\cdot\underset{x\to0}{lim}\,(x)-5\cdot\big[\underset{x\to0}{lim}\,(x)\big]^2$

$\sf L=3-7\cdot0-5\cdot0^2$

$\sf L=3-0-5\cdot0$

$\sf L=3-0$

$\red{\sf L=3}$

Então o limite existe e é igual a 3.

Propriedades usadas:

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

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

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

• $\sf \underset{x\to a}{lim}\,(k)=k$

• $\sf \underset{x\to a}{lim}\,(x)=a$