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JEE Main & Advanced Sample Paper JEE Main Sample Paper-20

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

    A) \[1/4\]                                 

    B) \[3/4\]

    C) \[1/2\]                                 

    D) \[1\]

    Correct Answer: B

    Solution :

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


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