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$Let f : R \to R be defined by f (x) = \{\begin{array}{cc} α + \frac{\sin [x]}{x} & if x > 0 \\ 2 & if x = 0 Where [x] denotes the \\ β + [\frac{\sin x - x}{x^{3}}] x < 0 \end{array}$ $integral part of x . If f is continuous at x = 0 then β - α =$

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Correct option is B

Ltx→0 fx=f0α+0=2=β−1⇒α=β−1⇒β−α=1

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Let f:R→R be defined by f(x)=α+sin⁡[x]x if x>02 if x=0 Where [x] denotes the β+sin⁡x−xx3x<0 integral part of x. If f is continuous at x=0 then β−α=

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$Let f : R \to R be defined by f (x) = \{\begin{array}{cc} α + \frac{\sin [x]}{x} & if x > 0 \\ 2 & if x = 0 Where [x] denotes the \\ β + [\frac{\sin x - x}{x^{3}}] x < 0 \end{array}$ $integral part of x . If f is continuous at x = 0 then β - α =$