Answer
$$\Delta y \approx 0.0225$$
Work Step by Step
$$\eqalign{
& y = \sqrt {3x - 2} ;{\text{ from }}x = 2{\text{ to }}x = 2.03 \cr
& {\text{Calculate }}f'\left( x \right){\text{ and }}dx \cr
& f\left( x \right) = \sqrt {3x - 2} \cr
& f'\left( x \right) = \frac{3}{{2\sqrt {3x - 2} }} \cr
& dx = \Delta x \cr
& dx = 2.03 - 2 \cr
& dx = 0.03 \cr
& \cr
& \Delta y \approx f'\left( x \right)dx = dy \cr
& \Delta y \approx \frac{3}{{2\sqrt {3x - 2} }}dx \cr
& {\text{Substitute }}dx = 0.03{\text{ and }}x = 2 \cr
& \Delta y \approx \frac{3}{{2\sqrt {3\left( 2 \right) - 2} }}\left( {0.03} \right) \cr
& \Delta y \approx 0.0225 \cr} $$
