JEE Main & Advanced Mathematics Functions Question Bank Continuity

  • question_answer
    If \[f(x)=\left\{ \begin{align}   & x+\lambda ,\ x\,<3 \\  & \,\,\,\,\,\,\,\,\,4,\,\,x=3 \\  & 3x-5,\,\,x>3 \\ \end{align} \right.\]is continuous at\[x=3\], then \[\lambda =\] [MP PET 1994, 2001; RPET 1999]

    A)            4

    B)            3

    C)            2

    D)            1

    Correct Answer: D

    Solution :

               By definition of continuity, we know that                    \[\underset{x\to 3+}{\mathop{\lim }}\,f(x)=f(3)=\underset{x\to 3-}{\mathop{\lim }}\,f(x)\]                    \[\Rightarrow \,\underset{x\to 3-}{\mathop{\lim }}\,f(x)=4\] or \[\underset{h\to 0}{\mathop{\lim }}\,3-h+\lambda =4\]            \[f(3)=3.7\]


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