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12th Class Mathematics Continuity and Differentiability Question Bank Case Based (MCQs) - Continuity

  • question_answer
    If the potter is trying to make a pot using the function\[f\left( x \right)=\left[ x \right]\], will he get a pot or not ? Why?

    A) Yes, because it is a continuous function

    B) Yes, because it is not continuous

    C) No, because it is a continuous function

    D) No, because it is not continuous

    Correct Answer: D

    Solution :

    \[f\left( x \right)=\left[ x \right]\] At integral value of x = a, f(x) is not continuous  \[L.H.Lt.=\underset{x\to {{a}^{-}}}{\mathop{Lt}}\,\left[ x \right]=a-1\] \[R.H.Lt.=\,\underset{x\to {{a}^{+}}}{\mathop{Lt}}\,\left[ x \right]=a\] \[L.H.Lt.\,\ne R.H.Lt.\] \[\Rightarrow \,\,f\left( x \right)\] is not continuous.


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