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Use the Wronskian to determine whether the functions $y_1 = \sin\!\left(3x\right)$ and $y_2 = \cos\!\left(4x\right)$ are linearly independent.

Wronskian = $\mathrm{det}$

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=

These functions are linearly independent because the Wronskian is nonzero for value(s) of $x$ .