Pieces of a Limit

Calculus Level 2

If the limit

\[\lim _{ x\rightarrow 0 }{ \left( \frac { \sin { 2x } }{ { x }^{ 3 } } +a+\frac { b }{ { { x }^{ 2 } } } \right) } =0\]

is true for constants \(a\) and \(b\), then what is the value of \(3a+b?\)

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