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If the function f(x) = {{:((sin(k+1)x + ...

If the function `f(x) = {{:((sin(k+1)x + sinx)/x, "when " x lt 0),(1//2, "when " x=0 is),((x+2x^(2))^(1//2)/(2x^(3//2)), " when " x gt 0):}`
continous at `x=0`, then the value of k is-

A

`1//2`

B

`-1//2`

C

`-3//2`

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
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