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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2000

  • question_answer
    If\[f(x)=\frac{3x+{{\tan }^{2}}x}{x}\]is continuous at\[x=0,\]then\[f(x)\]is equal to:

    A)  1                            

    B)         2

    C)  4                            

    D)         0

    E)  3

    Correct Answer: E

    Solution :

    \[f(x)=\frac{3x+{{\tan }^{2}}x}{x}\]is continuous at\[x=0\] \[\underset{x\to 0}{\mathop{\lim }}\,f(x)=\underset{x\to 0}{\mathop{\lim }}\,\frac{3x+{{\tan }^{2}}x}{x}\]                 \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{3+2\tan x{{\sec }^{2}}x}{1}\]                 \[=3\] \[\therefore \]                  \[f(0)=3\]


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