Question

Evaluate : $\underset{x\to \infty }{lim}\frac{3x^3-2x^2-1}{x^3+x^2+1}$

Answer 1

We have,

$\underset{x\to \infty }{lim}\frac{3x^3-2x^2-1}{x^3+x^2+1}$

$\underset{x\to \infty }{lim}\frac{x^3(3-\frac{2}{x^2}-\frac{1}{x^3})}{x^3(1+\frac{1}{x^2}+\frac{1}{x^3})}$

$\underset{x\to \infty }{lim}\frac{(3-\frac{2}{x^2}-\frac{1}{x^3})}{(1+\frac{1}{x^2}+\frac{1}{x^3})}$

$\Rightarrow \frac{(3-\frac{2}{{\infty }^2}-\frac{1}{{\infty }^3})}{(1+\frac{1}{{\infty }^2}+\frac{1}{{\infty }^3})}$

$\Rightarrow \frac{3-0-0}{1+0+0}$

$\Rightarrow 3$

Hence, this is the answer.