By Ron Larson, Bruce H. Edwards
Designed for the three-semester engineering calculus direction, CALCULUS: EARLY TRANSCENDENTAL features, 6th variation, maintains to supply teachers and scholars leading edge educating and studying assets. The Larson staff continually has major ambitions for textual content revisions: to boost unique, readable fabrics for college students that essentially outline and exhibit recommendations and principles of calculus; and to layout accomplished instructing assets for teachers that hire confirmed pedagogical options and retailer time. The Larson/Edwards Calculus software deals an answer to deal with the wishes of any calculus direction and any point of calculus pupil. each version from the 1st to the 6th of CALCULUS: EARLY TRANSCENDENTAL features has made the mastery of conventional calculus talents a concern, whereas embracing the easiest positive aspects of latest expertise and, whilst acceptable, calculus reform rules.
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Additional info for Calculus: Early Transcendental Functions (6th Edition)
15. ͑1, 7͒ m ϭ Ϫ3 16. ͑Ϫ2, Ϫ2͒ mϭ2 31. y ϭ Ϫ3 32. x ϭ 4 33. y ϭ Ϫ2x ϩ 1 1 34. y ϭ 3 x Ϫ 1 3 35. y Ϫ 2 ϭ 2 ͑x Ϫ 1͒ 36. y Ϫ 1 ϭ 3͑x ϩ 4͒ 37. 2x Ϫ y Ϫ 3 ϭ 0 38. x ϩ 2y ϩ 6 ϭ 0 Finding an Equation of a Line In Exercises 17–22, find an equation of the line that passes through the point and has the indicated slope. Then sketch the line. Point Slope 17. ͑0, 3͒ mϭ 19. ͑0, 0͒ mϭ 21. ͑3, Ϫ2͒ mϭ3 3 4 2 3 Point 18. ͑Ϫ5, Ϫ2͒ Slope Finding an Equation of a Line In Exercises 39–46, find m is undefined. an equation of the line that passes through the points.
To find the range, observe that f ͑x͒ ϭ Ίx Ϫ 1 is never negative. 23(a). b. The domain of the tangent function f ͑x͒ ϭ tan x f(x) = tan x is the set of all x-values such that 3 Range 2 x 1 x π 2π ϩ n, n is an integer. 23(b). For a review of the characteristics of this and other trigonometric functions, see Appendix C. A Function Defined by More than One Equation (b) The domain of f is all x-values such that ϩ n, and the range is ͑Ϫ ϱ, ϱ͒. 23 For the piecewise-defined function f ͑x͒ ϭ Ά1 Ϫx Ϫx, 1, Ί x < 1 x Ն 1 f is defined for x < 1 and x Ն 1.
Sketching a Graph A student who commutes 27 miles to attend college remembers, after driving a few minutes, that a term paper that is due has been forgotten. Driving faster than usual, the student returns home, picks up the paper, and once again starts toward school. Sketch a possible graph of the student’s distance from home as a function of time. find the domain of the function. 23. f ͑x͒ ϭ Ίx ϩ Ί1 Ϫ x 24. f ͑x͒ ϭ Ίx2 Ϫ 3x ϩ 2 25. g͑x͒ ϭ 2 1 Ϫ cos x 26. h͑x͒ ϭ 27. f ͑x͒ ϭ 1 xϩ3 28. g͑x͒ ϭ Խ Խ 1 sin x Ϫ ͑1͞2͒ 1 x2 Ϫ 4 Խ Խ Finding the Domain and Range of a Piecewise Function In Exercises 29–32, evaluate the function as Using the Vertical Line Test In Exercises 43–46, use the Vertical Line Test to determine whether y is a function of x.