KCET · Maths · Sets and Relations
If \( f(x)=\left\{\begin{aligned} K x^{3} ; & \text { if } x \leq 2 \\ 3 ; & \text { if } x>2 \end{aligned}\right. \) is continuous at \( x=2 \), then the value of \( K \) is
- A \( 13 \)
- B \( 04 \)
- C 3/4
- D \( 4 / 3 \)
Answer & Solution
Correct Answer
(C) 3/4
Step-by-step Solution
Detailed explanation
Given that \( f(x)=\left\{\begin{array}{cc}K \chi^{2} & x \leq 2 \\ 3 & x>2\end{array}\right. \)
Since, \( f(x) \) is continuous at \( x=2 \). Then, L.H.L = R.H.L
So, \( \lim _{x \rightarrow 2} K x^{2}=\lim _{x \rightarrow 2} 3 \) \( \Rightarrow K \cdot 2^{2}=3 \Rightarrow K=\frac{3}{4} \)
Since, \( f(x) \) is continuous at \( x=2 \). Then, L.H.L = R.H.L
So, \( \lim _{x \rightarrow 2} K x^{2}=\lim _{x \rightarrow 2} 3 \) \( \Rightarrow K \cdot 2^{2}=3 \Rightarrow K=\frac{3}{4} \)
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