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Q.

fx=32cot3xcot2x,                0

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a

a = 0

b

a = 2

c

b = -2

d

b = 2

answer is A.

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Detailed Solution

fπ-2=  limh→0  32cot3π2-hcot2π2-h                 = limh→0  22tan3h-cot2h                 =limh→0  32-tan3htan2h                 =  1fπ+2 = limh→0  1+cotπ2+hatanπ2+hb                 =limh→0  1+tan ha   cot hb                 =limh→0  elimh→0  1+tan  h-1a  cot  hb                 =  eabAlso,   fπ2=b+3fx  is   continuous   at   x=π2.   Therefore,1=b+3=eab    or   b=-2   and   a=0
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