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J & K CET Engineering J and K - CET Engineering Solved Paper-2006

  • question_answer
    \[\underset{x\to 1}{\mathop{\lim }}\,\frac{2{{x}^{2}}+x-3}{3{{x}^{2}}+2x-2}\]is equal to

    A)  \[1\]

    B)  \[2\]

    C)  \[-1\]

    D)  \[-2\]

    Correct Answer: A

    Solution :

    \[\underset{x\to 1}{\mathop{\lim }}\,\frac{2{{x}^{2}}+x-3}{3{{x}^{3}}-3{{x}^{2}}+2x-2}\] \[=\underset{x\to 1}{\mathop{\lim }}\,\frac{(2x+3)\,(x-1)}{(3{{x}^{2}}+2)(x-1)}\] \[=\underset{x\to 1}{\mathop{\lim }}\,\frac{2x+3}{3{{x}^{2}}+2}=\frac{5}{5}=1\]


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