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JEE Main & Advanced Mathematics Functions Question Bank Continuity

  • question_answer
    If \[f(x)=\left\{ \begin{align}   & \frac{{{x}^{2}}+3x-10}{{{x}^{2}}+2x-15},\ \ \text{when }x\ne -5 \\  & \,\,a\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,\text{when }x=-5 \\ \end{align} \right.\]is continuous at \[x=-5\], then the value of 'a' will be         [MP PET 1987]

    A)            \[\frac{3}{2}\]

    B)            \[\frac{7}{8}\]

    C)            \[\frac{8}{7}\]

    D)            \[\frac{2}{3}\]

    Correct Answer: B

    Solution :

               \[\underset{x\to \,-\,5}{\mathop{\lim }}\,f(x)=\frac{(x-2)\,\,(x+5)}{(x+5)\,(x-3)}=\frac{-7}{-8}=\frac{7}{8}.\]


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