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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 33

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

    A) 6

    B)        1

    C) -1

    D)        - 5

    Correct Answer: D

    Solution :

    The given expression (limit) is of \[\frac{0}{0}\] form. So, L? Hopital rule is applicable \[\therefore \,\,\,Given\,\,is\,\,\underset{x\to a}{\mathop{\lim }}\,\frac{f(a)g'(x)-g(a)f'(x)}{1}\] (By L/ Hospital?s Rule) \[=\,\,\underset{x\to a}{\mathop{\lim }}\,\frac{2g'(x)-3f'(x)}{1}=2g'(a)-3f'(a)\] \[=2\left( -1 \right)-3\left( 1 \right)=-\,5\]


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