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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2000

  • question_answer
    \[\underset{x\to 0}{\mathop{\lim }}\,\left( \frac{{{a}^{x}}-{{b}^{x}}}{x} \right)\]is equal to:

    A)  0                            

    B)         1

    C)  \[log\text{ }a-log\text{ }b\]   

    D)         \[log\text{ }a/log\text{ }b\]

    E)  does not exist

    Correct Answer: C

    Solution :

    \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{a}^{x}}-{{b}^{x}}}{x}=\underset{x\to 0}{\mathop{\lim }}\,\frac{{{a}^{x}}-x}{x}-\underset{x\to 0}{\mathop{\lim }}\,\frac{{{b}^{x}}-1}{x}\]


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