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Question

If limx1x2ax+bx1=5, then a+b is equal to :

A
1
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B
5
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C
4
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D
7
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Solution

The correct option is D 7
Given
limx1x2ax+bx1=5
In order to limit exist, numerator must be equal to 0 at x=1
(1)2a(1)+b=0
1a+b=0
ab=1 ...(1)

Now, applying L'hospital Rule
limx12xa1=5
2a=5
a=3 ...(2)
putting the value of a in (1)
b=4
a+b=7

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