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Question

If the function f(x)=2+cosx1(πx)2xπkx=π is continuous at x=π, then k equals :

A
0
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B
12
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C
2
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D
14
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Solution

The correct option is D 14
limxπ2+cosx1(πx)2=limxπ1+cosx(πx)2(2+cosx+1) [Rationalize numerator and denominator ]
=limxπ1cos(πx)(πx)2(2+cosx+1)
=limxπ2sin2(πx)2(πx)2(2+cosx+1)=14
So,k=14 .

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