KCET · Maths · Trigonometric Ratios & Identities
\[
\text { If } f(x)=\left\{\begin{array}{cc}
\frac{3 \sin \pi x}{5 x} ; & x \neq 0 \\
2 K ; & x=0
\end{array}\right.
\]
is continuous at \( x=0 \), then the value of \( K \) is
- A \( \frac{3 \pi}{10} \)
- B \( \frac{3 \pi}{5} \)
- C \( \frac{\pi}{10} \)
- D \( \frac{3 \pi}{2} \)
Answer & Solution
Correct Answer
(A) \( \frac{3 \pi}{10} \)
Step-by-step Solution
Detailed explanation
\(\lim_{x \to 0} f(x) = f(0)\) \(\lim_{x \to 0} \frac{3 \sin \pi x}{5x} = 2K\)
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