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JEE Main & Advanced Mathematics Limits, Continuity and Differentiability Question Bank Self Evaluation Test - Continuity and Differentiability

  • question_answer
    Let \[f(x)=\left\{ \begin{matrix}    3x-4, & 0\le x\le 2  \\    2x+\ell , & 2<x\le 9  \\ \end{matrix} \right.\] If f is continuous at x = 2, then what is the value of\[\ell \]?

    A) 0

    B) 2

    C) -2

    D) -1

    Correct Answer: C

    Solution :

    [c] Given function is: \[f(x)=\left\{ \begin{matrix}    3x-4, & 0\le x\le 2  \\    2x+\ell , & 2<x\le 9  \\ \end{matrix} \right.\] and also given that f(x) is continuous at \[x=2\]. For a function to be continuous at a point LHL = RHL = V.F. at that point. \[f(2)=2=V.F.\] \[\Rightarrow RHL:\underset{x\to 2}{\mathop{\lim }}\,(2x+\ell )=3(2)-4\] \[\Rightarrow \underset{h\to 0}{\mathop{\lim }}\,\left\{ 2(2+h)+\ell  \right\}=6-4\] \[\Rightarrow 4+\ell =2,\Rightarrow \ell =-2\]


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