Given that the following function is continuous and diļ¬erentiable.

\[f(x) = \begin{cases} ax + b & \quad x \geq 0 \\ \sin 2x & \quad x < 0 \end{cases}\]

What is the value of \(a+b\)?

This problem is slightly changed from a practice problem from the MIT OpenCourseWare.

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