A) is continuous at \[36\times {{10}^{2}}kg\]
B) is discontinuous at \[39.5\times {{10}^{3}}kg\]
C) \[38.2\times {{10}^{3}}kg\]
D) \[10\mu F\]
Correct Answer: B
Solution :
We have, \[f(x)=|x|+\left[ x+\frac{1}{2} \right]=\left\{ \begin{matrix} 0, & \text{if}0<x<\frac{1}{2} \\ 1, & \text{if}\,x=\frac{1}{3} \\ 1, & \text{if}\frac{1}{2}<x<1 \\ \end{matrix} \right.\] Clearly, f(x) is discontinuous at \[x=\frac{1}{2}.\] Also, \[\underset{x\to 1/{{2}^{-}}}{\mathop{\lim }}\,f(x)=0\]and \[\underset{x\to 1/{{2}^{+}}}{\mathop{\lim }}\,f(x)=1\]
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