Question

(1) A box has a height of 6 inches, a width of 4 inches, and a length of 10 inches (and therefore a volume of 240 cubic inches). The height is decreasing at a rate of 0.5 inches per minute, the width is increasing at a rate of 2 inches per minute, and the length is increasing at a rate of 1 inch per minute. At what rate is the volume changing?

Car A travels East towards the intersection of two roads at 30 mph. Car B travels North away from the intersection at a rate of 40mph. How quickly is the distance between the cars changing when A is 3 miles away from the intersection and B is 4 miles away from the intersection?

Use either a linear approximation or differentials to estimate the value of (8.1)^1/3

Find the following differentials. (a) d (e^sinx) (b) d (cos xy) (c) d (x/yⁿ ) where n is a constant. Simplify your answer, ending with a single fraction.

Answer 1

vem) ILOん V: ケt 24 120 -20 mu 07 on

しじけ、ng Value el in Cls 180十220 SD m |ん.

及 ว้เ-a Sinx. LE dr วา dl