# #2015_29 Continuity at a point

Calculus Level 3

$\large{ f(x) = \begin{cases} \dfrac{1-\sin^3(x)}{3\cos^2(x)} & \text{for } x<\dfrac\pi2 \\ a & \text{for } x=\dfrac\pi2 \\ \dfrac{b(1-\sin(x))}{(\pi-2x)^2} & \text{for } x>\dfrac\pi2\\ \end{cases}}$

Find the sum of values of $a$ and $b$ such that the function $f(x)$ above is continuous at $x=\dfrac { \pi }{ 2 }$.

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