BCECE Engineering BCECE Engineering Solved Paper-2011

  • question_answer
    If \[\underset{x\to 0}{\mathop{\lim }}\,\phi (x)={{a}^{3}},a\ne 0,\] then \[\underset{x\to 0}{\mathop{\lim }}\,\phi (x/a)\] is equal to

    A)  \[{{a}^{2}}\]                                         

    B)         \[1/{{a}^{3}}\]

    C)         \[1/{{a}^{2}}\]                     

    D)         \[{{a}^{3}}\]

    Correct Answer: D

    Solution :

    \[\underset{x\to 0}{\mathop{\lim }}\,\phi \text{=}\underset{t\to 0}{\mathop{\lim }}\,\phi \left( \frac{at}{a} \right)\] (put \[x=at\]then \[t\to 0\]as \[x\to 0\])                 \[=\underset{t\to 0}{\mathop{\lim }}\,\phi (t)\,=\text{ }\underset{x\to 0}{\mathop{\lim }}\,\phi (x)={{a}^{3}}\]


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