Question

$\underset{x\to 0}{lim}\frac{e^{3x}-1}{\log (1+5x)}=$

• A. $\frac{5}{3}$
• B. $\frac{3}{5}$
• C. $-\frac{3}{5}$
• D. none of these

Answer 1

The correct option is B $\frac{3}{5}$

Now,

$\underset{x\to 0}{lim}\frac{e^{3x}-1}{\log (1+5x)}$

$=\frac{\underset{x\to 0}{lim}\frac{e^{3x}-1}{x}}{\underset{x\to 0}{lim}\frac{\log (1+5x)}{x}}$

$=\frac{3\times \underset{3x\to 0}{lim}\frac{e^{3x}-1}{3x}}{5\times \underset{5x\to 0}{lim}\frac{\log (1+5x)}{5x}}$

$=\frac{3\times 1}{5\times 1}$

$=\frac{3}{5}$.