CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2011

  • question_answer
    \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{(1+2x)}^{10}}-1}{x}\]is equal to

    A)  5                                            

    B)  10

    C)  15                         

    D)         20

    E)  0

    Correct Answer: D

    Solution :

    \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{(1-2x)}^{10}}-1}{x}\]                            \[\left( \frac{0}{0}form \right)\] Using L hospital rule, \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{10{{(1+2x)}^{9}}(2)-0}{1}\]                 \[=10{{(1+0)}^{9}}.2=20\]


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