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Question

If n is the number of real solutions of the equation min(e|x|,1e|x|)=14 and L=limx0(e2x1x+e3x1x+e4x1x+ upto n terms), then the value of L is

A
5
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B
7
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C
10
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D
14
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Solution

The correct option is D 14
For intersection point,
1e|x|=e|x|
e|x|=12
|x|=ln2
x=ln2,ln2


Using the graph,
Number of solutions =4

L=limx0(e2x1x+e3x1x+e4x1x+e5x1x)
=limx0(2e2x12x+3e3x13x+4e4x14x+5e5x15x)
Since limx0eax1ax=1
L=2+3+4+5=14

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