Question

${lim}_{x\to 0}\frac{\sin 7x}{\sin 3x}$ equals

• A. $\frac{7}{3}$
• B. $\frac{10}{3}$
• C. $\frac{14}{3}$
• D. $\frac{1}{3}$

Answer 1

The correct option is A $\frac{7}{3}$

We have,

${lim}_{x\to 0}\frac{\sin 7x}{\sin 3x}$

${lim}_{x\to 0}\frac{\sin 7x}{\sin 3x}$

${lim}_{x\to 0}\frac{\frac{\sin 7x}{7x}\times 7x}{\frac{\sin 3x}{3x}\times 3x}$

${lim}_{x\to 0}\frac{\frac{\sin 7x}{7x}\times 7}{\frac{\sin 3x}{3x}\times 3}$

$=\frac{1\times 7}{1\times 3}$

$=\frac{7}{3}$

Hence, this is the answer.