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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 toA. `alpha-1`B. `alpha+1`C. `alpha+2`D. `alpha-2` |
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Answer» Correct Answer - 2 `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` |
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