A function f is defined by f(x)= {{:(...

A function f is defined by
`f(x)= {{:((sin (a + 1) x + sinx)/(x)" if " x lt 0),(c " if " x = 0),(((x + bx^(2))^(1/2)- x^(1/2))/(bx^(3/2)) " if " x gt 0 ):}`
It f(x) is continuous at x = 0 , find the values of a,b and c .

A

`a = (-3)/(2) , c = (1)/(2) , b ne 0 `

B

` a = b = (1)/(2) , c = 0 `

C

` a = b = c = (1)/(2)`

D

`a = (1)/(2) b ne 0 c = 1 `

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The correct Answer is:

A

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