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An example of an operation we perform on two

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Unformatted text preview: function of x and state the applied domain. 5. Use a calculator to approximate (to two decimal places) the dimensions of the box which minimize the surface area. 2 In this case, long division amounts to term-by-term division. 4.3 Rational Inequalities and Applications 271 Solution. 1. We are told the volume of the box is 1000 cubic centimeters and that x represents the width, in centimeters. From geometry, we know Volume = width × height × depth. Since the base of the box is to be a square, the width and the depth are both x centimeters. Using h for the height, we have 1000 = x2 h, so that h = 1000 . Using function notation,3 h(x) = 1000 As for x2 x2 the applied domain, in order for there to be a box at all, x > 0, and since every such choice of x will return a positive number for the height h we have no other restrictions and conclude our domain is (0, ∞). 2. To solve h(x) ≥ x, we proceed as before and collect all nonzero terms on one side of the inequality and use a sign diagram. h(x) ≥ x 1000 ≥x x2...
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