JEE Main & Advanced Mathematics Differentiation Question Bank Derivative at a point Standard Differentiation

  • question_answer
    The derivative of function \[f(x)\] is \[{{\tan }^{4}}x\]. If \[f(0)=0\] then \[\underset{x\to 0}{\mathop{\lim }}\,\frac{f(x)}{x}\]is equal to [J & K 2005]

    A)            1

    B)          0

    C)            ?1

    D)            None of these

    Correct Answer: B

    Solution :

               \[\underset{x\to 0}{\mathop{\lim }}\,\frac{f(x)}{x}=\underset{x\to 0}{\mathop{\lim }}\,\frac{f(x)-0}{x-0}=\underset{x\to 0}{\mathop{\lim }}\,\frac{f(x)-f(0)}{x-0}\]                    \[={{\left. {f}'(x) \right|}_{x=0}}\]\[={{\left. {{\tan }^{4}}x \right|}_{x=0}}=0\]


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