1. Consider the area A of a square of side x. a)Find the rate of change of area
ID: 3287721 • Letter: 1
Question
1. Consider the area A of a square of side x. a)Find the rate of change of area with respect of side dA/dx. b)How fast is the area changing the instant the side has a length 10?(units square per foot) c)Use part b) to approximate the change in area when the side increases from to to 11 feet. d)Calculate directly how much the area changes when the side increases from 10 feet to 11 feet. e)Draw on one diagram a square whose side is length x and one whose side is length x+1? f)On the diagram of part e) shade the portion that gives the change in area. g)Give a formula for the size of the shaded area and relate it dA/dx. 2. Repeat question 1 with a cube considering its volume V in terms of the length of its side x. Complete parts a) though g) considering dV/dx and doing your best to draw a cube of side x and side x+1 on the same diagram. For those without great art skills, some words might help. Give the units in part b. Hopefully these exercises help to see why the derivative of x^2 is 2x and the derivative of x^3 is 3x^2.Explanation / Answer
area = x^2
dA/dx = 2x
b) dA/dx = 2 x 10 = 20
c) 11^2 - 10^2 = 121 - 100 = 21 ft^2
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