Let f(x)=⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩−2sinx if x≤ – InterviewSolution

1.	Let f(x)=⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩−2sinx if x≤−π2Asinx+B if −π2<x<π2cosxif x≥π2 For what values of A and B, the function f(x) is continuous throughout the real line ?
Answer» Let $f (x) = ⎧ ⎪⎪⎪⎪⎪⎪ ⎨ ⎪⎪⎪⎪⎪⎪ ⎩ \begin{matrix} - 2 sin x & if x \leq \frac{- π}{2} A sin x + B & if \frac{- π}{2} < x < \frac{π}{2} cos x & if x \geq \frac{π}{2} \end{matrix}$ For what values of $A$ and $B$ , the function $f (x)$ is continuous throughout the real line ?

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