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J & K CET Engineering J and K - CET Engineering Solved Paper-2005

  • question_answer
    The derivative of function \[f(x)\] is \[{{\tan }^{4}}x\]. If \[f(x)=0,\] then \[\underset{x\to 0}{\mathop{\lim }}\,\frac{f(x)}{x}\]is equal to

    A)  \[1\]             

    B)  \[0\]

    C)  \[-1\]            

    D)  none of these

    Correct Answer: B

    Solution :

    Given,    \[f(0)=0,\,\,f'(x)={{\tan }^{4}}x\] \[\therefore \] \[\underset{x\to 0}{\mathop{\lim }}\,\frac{f(x)}{x}=\underset{x\to 0}{\mathop{\lim }}\,\frac{f'(x)}{1}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{{{\tan }^{4}}x}{1}=0\]


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