Let f: R→R be defined byf(x)=⎧⎪⎪⎪⎨⎪⎪⎪⎩α+sin[x]2if – InterviewSolution

1.	Let f: R→R be defined byf(x)=⎧⎪⎪⎪⎨⎪⎪⎪⎩α+sin[x]2if x>0 2if x=0β+[sin x−xx3]if x<0where [y] denotes the integral part of y. If f is continuous at x=0, then β−α=
Answer» Let f: $R \to R$ be defined by $f (x) = ⎧ ⎪⎪⎪ ⎨ ⎪⎪⎪ ⎩ \begin{matrix} α + \frac{s i n [x]}{2} & i f x > 0 2 & i f x = 0 β + [\frac{s i n x - x}{x^{3}}] & i f x < 0 \end{matrix}$ where $[y]$ denotes the integral part of y. If f is continuous at $x = 0, t h e n β - α =$

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