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Q.

If f(x)=a+sin[x]x,x>02,x=0b+sinx−xx3,x<0   (where [.] denotes the greatest integer function). If f(x)  is continuous at x=0 , then b is equal to

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a

a−1

b

a+1

c

a+2

d

a−2

answer is B.

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Detailed Solution

f(0+)=x→0Lima+sin[x]x=a   since x→0Limsinx−xx3=−16;  we get f(0−)=b−1 Hence b=a+1
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