Question

The value of $\underset{x\to 0}{lim}\frac{\log (1+2x)}{x}$ is equal to :

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

Answer 1

The correct option is B $2$

The value of $\underset{x\to 0}{lim}\frac{\log (1+2x)}{x}$ is ....$\left(\text{form}\frac{0}{0}\right)$
$=\underset{x\to 0}{lim}\frac{\frac{2}{1+2x}}{1}=2$ ( L'Hospital's rule)