Chapter 12.4, Problem 56E

(a)

To determine

To compute: The partial derivatives of $V_x$ and $V_y$.

(b)

To determine

To estimate: The change in volume when x increases from $x=0.5\text{m}$ to $x=0.51\text{m}$ for a box with $h=1.5\text{m}$ by using the linear approximation.

(c)

To determine

To estimate: The change in volume of a box with $x=0.5\text{m}$ when h decreases from $h=1.5\text{m}$ to $h=1.49\text{m}$ and use linear approximation.

(d)

To determine

Whether the change in x for $10\%$ will always produce a change of $10\%$ in the total volume V for a fixed height.

(e)

To determine

To explain: The change in h for $10\%$ will always produce a change of $10\%$ in the total volume V for a fixed length.