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Vaibhav Mathur Grade: 12
        

Let for all n belonging to real number,n-2>=2ln n,then the minimum value of the area bound by the curve |y|+1/n<=e^ -|x| is 2 sq. unit. True or false

7 years ago

Answers : (1)

Ramesh V
70 Points
										

From n-2 >= 2*ln(n) 


we can say n> 0  which also mean:  n-1 > 0


Now from the curve

  |y|+1/n <= e-|x|   or           |y| <= e-|x| +1/n


 


Now the graph of e-|x|  is symmetric about Y axis 


for 1/n > 0 ;


CASE 1: lets  take least value 1/n = 0


so,   |y| <= e-|x|



For , |y| <= e-|x|  the area bounded is  2*integral of e-|x| with limits from 0 to infininty


so area is 2 sq. units


 


CASE 1: lets  take  value 1/n more than 0


 


So so |y| <= e-|x| - 1/n


here e-|x| - 1/n becomes negative as shown in graph


but |y| is always positive which can never be less than a negative no.


so case 2 is not possible


hence area bounded is 2 sq. units and its TRUE

7 years ago
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