If `f(x)={alpha+sin[x]/x , x > 0 and 2 ,x=0 and beta+[(sin x-x)/x^3] ,x < 0` (whlenotes the greatest integer function) if `f(x)` is continuous at `x = 0`. then `beta` is equal to

Options

A. `alpha-1`
B. `alpha+1`
C. `alpha+2`
D. `alpha-2`

Answer

2

Explanation

`f(0)=2`
`f(0+)=underset(4rarr0)lim alpha + (sin[h])/(h) = alpha`
`f(0^(-))=beta+underset(hto0)(lim)[((h-(h^(3))/(31)....)-h)/(h^(3))]=beta-1`
`alpha=2, beta-1 = 2 rArr beta =3`