67. A wire is stretched horizontally, as shown in the accompanying figure. An experiment is conducted...

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67. A wire is stretched horizontally, as shown in the accompanying figure. An experiment is conducted in which different weights are attached at the center and the corresponding vertical displacements are measured. When too much weight is added, the wire snaps. Based on the data in the following table, what do you think is the maximum possible displacement for this kind of wire? Weight ab 15 16 17 | 18 |17.5 17.9 17.99 W (lb) Displacement 1.7 1.75 1.78 Snaps 1.79 1.795 Snaps y (in.) T y Work W wod ya d squads noi 10 92 EXERCISE 67 id be In Exercises 56 and 57, find the values of the constant A so that the function f(x) will be continuous for all x. (1 - 3x 56. f(x) = Ax + 2x - 3 Ax+2x-3 if x <4w to d if x 4 if x < 2 [Ax - 3 (3-x+2x if x 2 57. f(x) = S 58. Consider the equation 1 Leo Jedi gaivoid x-x-1= OST x + 1 a. Use the intermediate value property to show that the equation has a solution between x = 1 and x = 2. b. Is there a solution between x = 1.5 and x = 1.6? What about between x = 1.7 and x = 1.8? Explain. 59. Show that the equation x 8+ 9x2/3 = 29 has at least one solution for the interval 0 x 8. - x = 60. Show that the equation x = x + 2x - 1 must have at least one solution on the interval 0 x 1. - 1 to sdmun ad 1970 2200 0% 67. A wire is stretched horizontally, as shown in the accompanying figure. An experiment is conducted in which different weights are attached at the center and the corresponding vertical displacements are measured. When too much weight is added, the wire snaps. Based on the data in the following table, what do you think is the maximum possible displacement for this kind of wire? Weight ab 15 16 17 | 18 |17.5 17.9 17.99 W (lb) Displacement 1.7 1.75 1.78 Snaps 1.79 1.795 Snaps y (in.) T y Work W wod ya d squads noi 10 92 EXERCISE 67 id be In Exercises 56 and 57, find the values of the constant A so that the function f(x) will be continuous for all x. (1 - 3x 56. f(x) = Ax + 2x - 3 Ax+2x-3 if x <4w to d if x 4 if x < 2 [Ax - 3 (3-x+2x if x 2 57. f(x) = S 58. Consider the equation 1 Leo Jedi gaivoid x-x-1= OST x + 1 a. Use the intermediate value property to show that the equation has a solution between x = 1 and x = 2. b. Is there a solution between x = 1.5 and x = 1.6? What about between x = 1.7 and x = 1.8? Explain. 59. Show that the equation x 8+ 9x2/3 = 29 has at least one solution for the interval 0 x 8. - x = 60. Show that the equation x = x + 2x - 1 must have at least one solution on the interval 0 x 1. - 1 to sdmun ad 1970 2200 0%