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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2003

  • question_answer
    \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\tan x-\sin x}{{{x}^{3}}}\]is equal to:

    A)  0    

    B)                                         1                            

    C)  1/2                       

    D)        \[-1/2\]

    E)  \[\infty \]

    Correct Answer: C

    Solution :

    \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\tan x-\sin x}{{{x}^{3}}}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin x(1-\cos x)}{{{x}^{3}}}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{\tan x}{x}.\frac{2{{\sin }^{2}}x/2}{4.{{(x/2)}^{2}}}\] \[=\frac{1}{2}\]


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