If $ f(x)=\left\{\begin{aligned} K x^{3} ; & \text { if } x \leq 2 \ 3 ; & \text { if } x2 \end{aligned}\right. $ is continuous at $ x=2 $, then the value of $ K $ is

Question

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, $ 13 $, $ 04 $, 3/4, $ 4 / 3 $

MARKS App · Accepted Answer

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} $

Search any question & find its solution

Looking for more such questions to practice?