Question

Solve

$\underset{x\to 0}{lim}\frac{\sin 5x}{\tan 3x}$

• A. $-\frac{5}{3}$
• B. $\frac{5}{3}$
• C. $\frac{7}{3}$
• D. None of these

Answer 1

Answer: (B)

$\frac{5}{3}$

Let$L=\underset{x\to 0}{lim}\frac{\sin 5x}{\tan 3x}$

$=\underset{x\to 0}{lim}\frac{\sin 5x}{5x}\times \frac{3x}{\tan x}\times \frac{5}{3}$

we know that $\underset{x\to 0}{lim}\frac{\sin 5x}{5x}=1$ and $\underset{x\to 0}{lim}\frac{3x}{\tan 3x}=1$

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

$\underset{x\to 0}{lim}\frac{\sin 5x}{\tan 3x}=\frac{5}{3}$