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Question

Let f(x)=⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪(1cos4x)tanxx3if x<02a2if x=0x16+x4if x>0
The possible value of a so that f is continuous is

A
4
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B
2
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C
2
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D
not possible
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Solution

The correct options are
B 2
C 2
limx0f(x)=limx0(1cos4x)x2tanxx=limx02sin22xx2tanxx
=limx0sin22x(2x)2.4tanxx
limx0+f(x)=limx0+x16+x4
=limx0+x16+x16.16+x+4
=limx0+(16+x+4)=8,
Thus 2a2=8a=±2

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