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JEE Main & Advanced Mathematics Functions Question Bank Limits

  • question_answer
    If \[f(a)=2,\ f'(a)=1,\ g(a)=-1;\ g'(a)=2\], then \[\underset{x\to a}{\mathop{\lim }}\,\frac{g(x)f(a)-g(a)f(x)}{x-a}=\] [DCE 1999; Karnataka CET 1999; MP PET 1995; Pb. CET 2004]

    A)                 3

    B)                 5

    C)                 0

    D)                 ?3

    Correct Answer: B

    Solution :

                       \[\underset{x\to a}{\mathop{\lim }}\,\,\frac{f(a)\,[g(x)-g(a)]-g(a)\,[f(x)-f(a)]}{[x-a]}\]                                                 \[=f(a){g}'(a)-g(a){f}'(a)=2\times 2-(-1)\,(1)=5.\]


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