CUET · MATHS · PYQ PAPER 2025
If the function \(f(x)=\left\{\begin{array}{ll}\frac{\sin 3 x}{x}, & \text { if } x \neq 0 \\ \frac{3 k}{2}, & \text { if } x=0\end{array}\right.\) is continuous at \(x=0\), then the value of \(k\) is :
- A \(\frac{2}{3}\)
- B 4
- C 2
- D 9
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
\( \lim_{x \to 0} f(x) = f(0) \) \( \lim_{x \to 0} \frac{\sin 3x}{x} = \frac{3k}{2} \) \( 3 = \frac{3k}{2} \) \( 6 = 3k \) \( k = 2 \)
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