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JEE Main & Advanced AIEEE Solved Paper-2003

  • question_answer
    Let f(a) = g(a) = k and their nth derivatives \[{{f}^{n}}(a),\,{{g}^{n}}(a)\] exist and are not equal for some n. Further, if \[\underset{x\to a}{\mathop{\lim }}\,\frac{f(a)\,g(x)-i(a)-g(a)f(x)+g(a)}{g(x)-f(x)}=4\], then the value of k is equal to     AIEEE  Solved  Paper-2003

    A) 4             

    B)       2                             

    C) 1                             

    D) 0

    Correct Answer: A

    Solution :

    \[\underset{x\to a}{\mathop{\lim }}\,\frac{f(a)\,g(x)-f(a)-g(a)f(x)+g(a)}{g(x)-f(x)}=4\] Applying L' Hospital rule,                     \[\underset{x\to a}{\mathop{\lim }}\,\frac{f(a)\,g'(x)-g(a)f'(x)}{g'(x)-f'(x)}=4\] \[\Rightarrow \]   \[\underset{x\to a}{\mathop{\lim }}\,\frac{k\,g'(x)-kf'(x)}{g'(x)-f'(x)}=4\] \[\Rightarrow \]                                   k = 4


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