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Question

If the function f(x)=⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ ⎪1cos2pxx2,x<0q2,x=011xx,x>0 is continuous at x=0, then the value(s) of 2(p+q2) can be

A
0
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B
1
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C
2
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D
4
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Solution

The correct option is C 2
For function to be continuous at x=0
R.H.L.=L.H.L=f(0)
Now, R.H.L.=limx0+11xx×1+1x1+1x
=limx0+xx(1+1x)
R.H.L.=12=q2

L.H.L.=limx01cos2pxx2
=limx02sin2pxx2=2p2
2p2=12
p=±12
2(p+q2)=±1+1=0 or 2

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