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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Self Evaluation Test - Application of Derivatives

  • question_answer
    Area of the triangle formed by the normal to the curve \[x={{e}^{\sin \,}}^{y}\] at (1, 0) with the coordinate axes is:

    A) ¼

    B)  ½

    C) 3/4

    D) 1

    Correct Answer: B

    Solution :

    [b] \[x={{e}^{\sin \,\,y}}\Rightarrow In\,\,x=\sin \,\,y\Rightarrow \frac{1}{x}\frac{dx}{dy}=\cos y\] \[\therefore \] slope of normal at (1, 0) \[=-\frac{dx}{dy}=-1\times \cos 0=-1\] \[\therefore \] Equation of normal is \[y-0=-1(x-1)\] \[\Rightarrow x+y=1\] Which forms triangle of area \[\frac{1}{2}\] with axes.


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