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11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-4

  • question_answer
    \[\underset{x\to \infty }{\mathop{\lim }}\,\frac{\mathbf{2}{{\mathbf{x}}^{\mathbf{3}}}-\mathbf{4x}+\mathbf{7}}{3{{x}^{3}}+5{{x}^{2}}-4}\]Is equal to

    A) \[\frac{3}{2}\]                          

    B) \[\frac{2}{3}\]              

    C)  0                                

    D) ¥

    Correct Answer: B

    Solution :

    [b]\[=\underset{x\to \infty }{\mathop{\lim }}\,\frac{2{{x}^{3}}-4x+7}{3{{x}^{3}}+5x-4}\] Dividing numerator & denominator by \[{{x}^{3}},\]we have \[=\underset{x\to \infty }{\mathop{\lim }}\,\frac{2-\frac{4}{{{x}^{2}}}+\frac{7}{{{x}^{3}}}}{3+\frac{5}{x}-\frac{4}{{{x}^{3}}}}=\frac{2}{3}\] Hence, option [b]be current.


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