Question

Value of $\underset{x\to \infty }{\text{lim}}{\left(\frac{x^2+2x-1}{2x^2-3x-2}\right)}^{\frac{2x+1}{2x-1}}$ is

• A. $0$
• B. $-2$
• C. $\frac{1}{2}$
• D. It does not exist

Answer 1

The correct option is C $\frac{1}{2}$

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