Find - and - so that the function f x defined by f x - - 2sin x- for - - x - - - 2 - -sin x - - - for - - 2 - x - - 2 - cos x- for - 2- x -is continuous on - - - -

f( π #160; 2 )= 2sin ( π #160; 2 ) =2 f( π #160; 2 +h)=αsin ( π #160; 2 +h) +β =β α =2 (i) f(π #160; 2 h)=α + ...

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Theorems for Continuity

Find α and ...

Question

Find $α$ and $β$ , so that the function $f (x)$ defined by
$f (x) = - 2 sin x,$ for $- π \leq x \leq - \frac{π}{2}$
$= α sin x + β,$ for $- \frac{π}{2} < x < \frac{π}{2}$
$= cos x,$ for $\frac{π}{2} \leq x \leq π$
is continuous on $[- π, π]$ .

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