Question

Evaluation of exponential & logarithmic limits : $\underset{x\to \infty }{Lt}x\left[\log \right(x+1)-\log x]=?$

• A. $e^2$
• B. $e$
• C. $1$
• D. $1/e$

Answer 1

The correct option is C $1$

$\underset{x\to \infty }{lim}x\left[\log \right(x+1)-\log x]=\underset{x\to \infty }{lim}\frac{\log (1+\frac{1}{x})}{\frac{1}{x}}=$Indeterminate form

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