If fx=x-ex+cos2xx2, x≠0, is contitnuous at x=0, then where [x] and {r} denote the greatest integer and fractional part functions, respectively.
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a
f0=52
b
f0=-2
c
f0=0
d
f0f0=-1.5
answer is D.
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Detailed Solution
limx→0 x-ex+1-1-cos2xx2 =limx→0 x--ex+1x2-1-cos2xx2 =limx→0 x+1-1+x+x22x2-2sin2xx2 Using expansion of ex =-12-2 =-52Hence, for continuity , f0=-52.Now, f0=-3; f0=-52=12.Hencee, f0f0=-32=-1.5