Answer: the approximate change is \(0.274h\).

We start with the main method. For a small change, use \(\Delta y\approx (dy/dx)\Delta x\) evaluated at the starting value.

The function is

\(y=\cos x\sin^2x.\)

Differentiate using the product rule:

\(\frac{dy}{dx}=(-\sin x)\sin^2x+\cos x(2\sin x\cos x).\)

So

\(\frac{dy}{dx}=2\sin x\cos^2x-\sin^3x.\)

For a small increase from \(3\) to \(3+h\),

\(\delta y\approx h\left.\frac{dy}{dx}\right|_{x=3}.\)

Thus

\(\delta y\approx h\left(2\sin3\cos^23-\sin^33\right).\)

Evaluating the coefficient,

\(2\sin3\cos^23-\sin^33=0.273808\ldots\)

Therefore the approximate change in \(y\) is

\(0.274h\) to 3 significant figures.

This completes the solution and gives the required result.