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Question

Let f(x)=xsinπx,x>0. Then for all natural numbers n, f(x) vanishes at

A
A unique point in the interval (n+12,n+1)
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B
A unique point in the interval (n,n+1)
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C
A unique point in the interval (n+12,n+1)
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D
A unique point in the interval (n,n+12)
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Solution

The correct option is C A unique point in the interval (n+12,n+1)
f(x)=xsinπx
f(x)=sinπx+πxcosπx=0
tanπx=πx

Clear f(x) has one root in (n+12,n+1), also f(x) has one root in (n,n+1).

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