Q117 / 160 · WBJEE 2011 · Mathematics

\(f(x)=\left\{\begin{array}{cc}{[x]+[-x],} & \text { when } x \neq 2 \\ \lambda & \text { when } x=2\end{array}\right.\) If \(f(x)\) is continuous at \(x=2\), the value of \(\lambda\) will be

  • Correct answer
    A
    -1
  • B
    1
  • C
    0
  • D
    2

Solution

Hints: \(\mathrm{LHL}=\operatorname{Lt}_{\mathrm{h} \rightarrow 0}[2-\mathrm{h}]+[-(2-\mathrm{h})]\) \(=\operatorname{Lt}_{\mathrm{h} \rightarrow 0} 1+(-2+\mathrm{h})=1-2=-1\) \(\begin{aligned} & \mathrm{RML}=\underset{\mathrm{h} \rightarrow 0}{\operatorname{Lt}}[2+\mathrm{h}]+(-(2+\mathrm{h})) \\ & =2+(-2-\mathrm{h})=2-3=-1 \\ & \lambda=-1 \end{aligned}\)

Hence, the correct answer is option: 'A'.

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