Question

$\underset{x\to \infty }{lim}f\left(x\right)$, where $\frac{2x-3}{x}<f\left(x\right)<\frac{2x^2+5x}{x^2}$, is ............

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B 2

$\frac{2x-3}{x}<f\left(x\right)<\frac{2x^2+5x}{x^2}$

$\Rightarrow \underset{x\to \infty }{lim}\frac{2x-3}{x}<\underset{x\to \infty }{lim}f\left(x\right)<\underset{x\to \infty }{lim}\frac{2x^2+5x}{x^2}\Rightarrow \underset{x\to \infty }{lim}\frac{2-\frac{3}{x}}{1}<\underset{x\to \infty }{lim}f\left(x\right)<\underset{x\to \infty }{lim}\frac{2+\frac{5x}{x^2}}{1}\Rightarrow \underset{x\to \infty }{lim}f\left(x\right)=2$
Hence, option 'B' is correct.