By Ron Larson, Bruce H. Edwards

The Larson CALCULUS software has a protracted historical past of innovation within the calculus industry. it's been generally praised by way of a iteration of scholars and professors for its sturdy and potent pedagogy that addresses the wishes of a wide variety of educating and studying kinds and environments. each one identify is only one part in a finished calculus path software that rigorously integrates and coordinates print, media, and expertise items for winning educating and studying.

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F ͑x͒ ϭ Ίx ϩ 5 (a) f ͑Ϫ4͒ (b) f ͑Ϫ3͒ (b) f ͑11͒ (c) f ͑b͒ (c) f ͑Ϫ8͒ (d) f ͑x Ϫ 1͒ 5. g͑x͒ ϭ 5 Ϫ x2 (d) f ͑x ϩ ⌬x͒ 6. g͑x͒ ϭ ͑x Ϫ 4͒ x2 (c) g͑Ϫ2͒ (c) g͑c͒ (d) g͑t Ϫ 1͒ (d) g͑t ϩ 4͒ 7. f ͑x͒ ϭ cos 2x 8. f ͑x͒ ϭ sin x (a) f ͑͒ (b) f ͑Ϫ ͞4͒ (b) f ͑5͞4͒ (c) f ͑͞3͒ (c) f ͑2͞3͒ 9. f ͑x͒ ϭ x3 10. f ͑x͒ ϭ 3x Ϫ 1 f ͑x ϩ ⌬x͒ Ϫ f ͑x͒ ⌬x 1 Ίx Ϫ 1 f ͑x͒ Ϫ f ͑2͒ xϪ2 f ͑x͒ Ϫ f ͑1͒ xϪ1 12. f ͑x͒ ϭ x3 Ϫ x f ͑x͒ Ϫ f ͑1͒ xϪ1 In Exercises 13 –20, find the domain and range of the function. 14. g͑x͒ ϭ 4x2 15. g͑x͒ ϭ Ί6x 17.

88. The distance from the origin is K ͑K from ͑2, 0͒. 2 Preparation for Calculus Linear Models and Rates of Change ■ ■ ■ ■ ■ Find the slope of a line passing through two points. Write the equation of a line with a given point and slope. Interpret slope as a ratio or as a rate in a real-life application. Sketch the graph of a linear equation in slope-intercept form. Write equations of lines that are parallel or perpendicular to a given line. The Slope of a Line y y2 y1 The slope of a nonvertical line is a measure of the number of units the line rises (or falls) vertically for each unit of horizontal change from left to right.

Line: 3x Ϫ 4y ϭ 1 Line: x ϩ y ϭ 5 Line: 3x Ϫ 4y ϭ 10 93. Show that the distance between the point ͑x1, y1͒ and the line Ax ϩ By ϩ C ϭ 0 is Distance ϭ ԽAx1 ϩ By1 ϩ CԽ. ΊA2 ϩ B2 94. Write the distance d between the point ͑3, 1͒ and the line y ϭ mx ϩ 4 in terms of m. Use a graphing utility to graph the equation. When is the distance 0? Explain the result geometrically. 95. Prove that the diagonals of a rhombus intersect at right angles. ) 96. Prove that the figure formed by connecting consecutive midpoints of the sides of any quadrilateral is a parallelogram.