Question

Assertion :$\underset{x\to 0}{lim}\frac{\sin ax}{\sin bx}=\frac{a}{b}$, $a,b\ne 0$ Reason: $\underset{x\to 0}{lim}\frac{\sin x}{x}=1$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$\underset{x\to 0}{lim}\frac{\sin ax}{\sin bx}=\frac{{lim}_{x\to 0}\frac{\sin ax}{ax}}{{lim}_{x\to 0}\frac{\sin bx}{bx}}\times \frac{ax}{bx}=\frac{a}{b}$
Further $\underset{x\to 0}{lim}\frac{\sin x}{x}=1$ is true.
Hence, option 'A' is correct.