#2015_29 Continuity at a point

Calculus Level 3

Find the sum of values of \(a\) and \(b\) so that the function, \[\large{ f(x) = \begin{cases} \frac{1-\sin^3(x)}{3\cos^2(x)} &,& x<\frac\pi2\\ a & ,& x=\frac\pi2\\ \frac{b(1-\sin(x))}{(\pi-2x)^2} &,& x>\frac\pi2\\ \end{cases}} \] is continuous at \(x=\frac { \pi }{ 2 } \).

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