Evaluate `underset(xto0)lim(5sinx-7sin2x+3sin3x)/(x^(2)sinx).`

Explanation

To evaluate the limit

\[ \lim_{x \to 0} \frac{5\sin x - 7\sin 2x + 3\sin 3x}{x^2 \sin x}, \]

we will use the Taylor series expansion for \(\sin x\) around \(x = 0\).

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