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If f(x) is continuous at x=0, where f(x...

If `f(x)` is continuous at `x=0`, where `f(x)={:{((sin (a+1)x+sin x)/(x)", for " x lt 0),(c", for " x=0),((sqrt(x+bx^(2))-sqrt(x))/(b sqrt(x))", for " x gt 0):}`, then

A

a=-3/2, b=0, c=1/2

B

a=-3/2, b=1 , c=1/2

C

a=-3/2 , b `epsilon` R , c=-1/2

D

none of these

Text Solution

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The correct Answer is:
C
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