Download Mathematics for the nonmathematician by Morris Kline PDF

By Morris Kline

Erudite and interesting evaluation follows improvement of arithmetic from historic Greeks, via heart a long time and Renaissance to the current. Chapters specialize in good judgment and arithmetic, the quantity, the elemental inspiration, differential calculus, the idea of likelihood, and lots more and plenty extra. routines and difficulties.

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This function is defined only for x-values for which 4 Ϫ 3x Ն 0. By solving this inequality, you can conclude that x Յ 43. So, the domain is the interval ͑Ϫ ϱ, 43͔. Now try Exercise 73. In Example 7(c), note that the domain of a function may be implied by the physical context. For instance, from the equation 4 V ϭ 3␲ r 3 you would have no reason to restrict r to positive values, but the physical context implies that a sphere cannot have a negative or zero radius. 4 Functions 45 Applications h r =4 r Example 8 The Dimensions of a Container You work in the marketing department of a soft-drink company and are experimenting with a new can for iced tea that is slightly narrower and taller than a standard can.

5, Ϫ6͒, m ϭ 1 ͑Ϫ8, 1͒, m is undefined. ͑1, 5͒, m is undefined. 48. ͑Ϫ5, 4͒, m ϭ 2 1 50. ͑7, Ϫ2͒, m ϭ 2 ͑3, Ϫ2͒, m ϭ 0 ͑10, Ϫ6͒, m ϭ Ϫ1 ͑0, Ϫ9͒, m ϭ Ϫ2 ͑Ϫ1, Ϫ6͒, m ϭ Ϫ 12 In Exercises 51– 64, find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m. Sketch the line. 51. ͑0, Ϫ2͒, m ϭ 3 53. ͑Ϫ3, 6͒, m ϭ Ϫ2 55. ͑4, 0͒, m ϭ Ϫ 13 57. 59. 60. 61. 63. 52. ͑0, 10͒, m ϭ Ϫ1 54. ͑0, 0͒, m ϭ 4 56. ͑8, 2͒, m ϭ 14 58. ͑Ϫ2, Ϫ5͒, m ϭ 34 ͑2, Ϫ3͒, m ϭ Ϫ 12 ͑6, Ϫ1͒, m is undefined.

Two nonvertical lines are perpendicular if and only if their slopes are negative reciprocals of each other. That is, m1 ϭ Ϫ1͞m2. Example 4 y 2x − 3y = 5 3 2 Finding Parallel and Perpendicular Lines Find the slope-intercept forms of the equations of the lines that pass through the point ͑2, Ϫ1͒ and are (a) parallel to and (b) perpendicular to the line 2x Ϫ 3y ϭ 5. 40 2x Ϫ 3y ϭ 5 Write original equation. Ϫ3y ϭ Ϫ2x ϩ 5 yϭ 2 3x Ϫ Subtract 2x from each side. 5 3 Write in slope-intercept form. 40. a.

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