By Geoffrey C. Berresford, Andrew M. Rockett

This article for the only semester utilized or company calculus direction makes use of fascinating real-world functions to interact scholars' curiosity and convey them the sensible aspect of calculus. Many purposes are monetary or company comparable, yet many functions during this textual content conceal general-interest subject matters besides, together with the starting to be inhabitants of Africa, the composition of the superb court docket, water scarcity, the quickest pitch in baseball, and toxins and the depletion of common assets. The 5th version keeps the hallmark positive aspects that experience made short utilized Calculus so renowned: modern and fascinating functions; cautious and potent use of expertise, together with built-in calculator assurance that's non-compulsory; consistent pedagogical reinforcement via part summaries, bankruptcy summaries, conscientiously annotated examples, and additional perform difficulties; and quite a few workouts and task recommendations together with workout units, tasks, and essays.

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**Example text**

Predict how the lines y ϭ x ϩ 4 and y ϭ x Ϫ 4 would look, and then check your prediction by graphing them. (continues) Applied Exercises 55. BUSINESS: Energy Usage A utility considers demand for electricity “low” if it is below 8 mkW (million kilowatts), “average” if it is at least 8 mkW but below 20 mkW, “high” if it is at least 20 mkW but below 40 mkW, and “critical” if it is 40 mkW or more. Express these demand levels in interval notation. ] 56. GENERAL: Grades If a grade of 90 through 100 is an A, at least 80 but less than 90 is a B, at least 70 but less than 80 a C, at least 60 but less than 70 a D, and below 60 an F, write these grade levels in interval form (ignoring rounding).

X ϩ y ϭ 0 26. x ϭ 2y ϩ 4 27. x Ϫ y ϭ 0 28. y ϭ 23(x Ϫ 3) xϩ2 29. y ϭ 3 x y 30. ϩ ϭ 1 2 3 2x Ϫyϭ1 31. 3 xϩ1 yϩ1 ϩ ϭ1 32. 2 2 y 1 33. 25 and y-intercept 3 34. Slope 2 3 and y-intercept Ϫ 8 35. Slope 5 and passing through the point (Ϫ 1, Ϫ 2) 36. Slope Ϫ 1 and passing through the point (4, 3) 1 Ϫ3 Ϫ2 Ϫ1 Ϫ1 1 2 3 x Ϫ3 Ϫ2 Ϫ1 Ϫ1 Ϫ2 Ϫ2 Ϫ3 Ϫ3 47. 1 2 3 1 2 3 x 48. y y 3 3 2 2 1 1 Ϫ3 Ϫ2 Ϫ1 Ϫ1 1 2 3 x Ϫ3 Ϫ2 Ϫ1 Ϫ1 Ϫ2 Ϫ2 Ϫ3 Ϫ3 x 49–50. Write equations for the lines determining the four sides of each figure.

Solving for y: Subtracting 2x from both sides of 2x ϩ 3y ϭ 12 3y ϭ Ϫ2x ϩ 12 2 yϭϪ xϩ4 3 Dividing each side by 3 gives the slope-intercept form y ϭ mx ϩ b Therefore, the slope is Ϫ 23 and the y-intercept is (0, 4). Practice Problem 6 Find the slope and y-intercept of the line x Ϫ y ϭ 2. 3 ➤ Solution on page 15 Linear Regression (Optional) Given two points, we can find a line through them, as in Example 4. However, some real-world situations involve many data points, which may lie approximately but not exactly on a line.