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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2003

  • question_answer
    If \[f(a)=2f(a)=1,\,g(a)=3,\,g(a)=-1\] then \[\underset{x\to a}{\mathop{\lim }}\,\frac{f(a)\,g\,(x)-f(x)\,g\,(a)}{x-a}\] equal to :

    A)  6                                            

    B)  1

    C)  -1                                          

    D)  -5

    Correct Answer: D

    Solution :

    We have \[\underset{x\to a}{\mathop{\lim }}\,=\frac{f(a)\,g(x)-f(x)g(a)}{x-a}\] As we see it is \[\frac{0}{0}\] form so applying L-Hospital rule we have                 \[\underset{x\to a}{\mathop{\lim }}\,=\frac{f(a)g(x)-f(x)g(a)}{1-0}\]                 \[=f(a)g\,(a)-f\,(a)\,g\,(a)\]                 \[=2(-1)-1\,(3)=-2-3=-5\]


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