Question

What is the value of $\underset{x\to \infty }{lim}\frac{2x^2+x+1}{3x^2-x-1}$?

• A. $\frac{3}{2}$
• B. $\frac{2}{3}$
• C. $-1$
• D. $-4$

Answer 1

The correct option is B $\frac{2}{3}$

Let $L={lim}_{x\to \infty }\frac{{2x}^2+x+1}{{3x}^2-x-1}$

$\Rightarrow L={lim}_{x\to \infty }\frac{2+\frac{1}{x}+\frac{1}{x^2}}{3-\frac{1}{x}-\frac{1}{x^2}}$

We know $x\to \infty \Rightarrow \frac{1}{x}\to 0,\frac{1}{x^2}\to 0$

Thus $L=\frac{2+0+0}{3-0-0}=\frac{2}{3}$

So, option B is correct.