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Question

limxsin1sin(x2+2x2+1) is equal to (where [.] and {.} denote greatest integer and fractional part function respectively)

A
limx[x2+2x2+1]
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B
limxx2+2x2+1
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C
limx{x2+2x2+1}
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D
limx{x2x2+1}
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Solution

The correct options are
A limx[x2+2x2+1]
B limxx2+2x2+1
C limx{x2x2+1}
limxsin1sin(x2+2x2+1)=limxsin1sin(1+2/x21+1/x2)

as x1x20

=sin1sin(1)=1

A.limx[x2+2x2+1]=limx[1+1x2+1]

as x1x2+10
=[1]=1

B. limx[x2+2x2+1]=limx1+2/x21+1/x2

=1+01+0=1

C.limx{x2+2x2+1}=limx(x2+2x2+1[x2+2x2+1])({x}=x[x])

From above results

=11=0

D.limx{x2x2+1}=limx(x2x2+1[x2x2+1])

=limx(11+1/x2[11x2+1])(0<(11x21)<1)[11x21]=0

=10=1

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