Question

$\underset{x\to \infty }{lim}\frac{x-\log x}{x+\log x}=$

• A. $1$
• B. $-1$
• C. $0$
• D. $2$

Answer 1

The correct option is A $1$

$\underset{x\to \infty }{lim}\frac{x-\log x}{x+\log x}=$
Since, it is of the form $\frac{\infty }{\infty }$ , so applying L-Hopital's rule
$={lim}_{x\to \infty }\frac{1-\frac{1}{x}}{1+\frac{1}{x}}$
$=1$