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f(x)={sin(⌊x2⌋π)x2−3x−18+ax3+bfor 0≤x≤12cos(πx)+tan−1xfor 1≤x≤2f(x) = \begin{cases} \dfrac{\sin (\lfloor x^2 \rfloor \pi)}{x^2-3x-18} +ax^3+b & \text{for } 0 \le x \le 1 \\ 2 \cos (\pi x)+ \tan^{-1} x & \text{for } 1 \le x \le 2 \end{cases} f(x)=⎩⎨⎧x2−3x−18sin(⌊x2⌋π)+ax3+b2cos(πx)+tan−1xfor 0≤x≤1for 1≤x≤2
If f(x)f(x)f(x) is differentiable in [0,2][0,2][0,2], find the value of ∣π4−b−a∣\left| \dfrac{\pi}{4} - b - a \right| ∣∣∣4π−b−a∣∣∣.
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