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# A first course in infinitesimal calculus by Daniel A. Murray

By Daniel A. Murray

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Example text

In calculus, however, we prefer to use the radian measure of an angle because it simplifies our work. 28 Chapter 0 Preliminaries y DEFINITION Radian Measure of an Angle s If s is the length of the arc subtended by a central angle u in a circle of radius r, then Arc length uϭ ¨ r 0 x s r (1) is the radian measure of u (see Figure 2).

X ϩ 13y Ϫ 5 ϭ 0 45. x ϩ y Ϫ 8 ϭ 0 and 6x Ϫ 8y ϭ 10 and y Ϫ 5 ϭ 0 62. 2x Ϫ 3y Ϫ 12 ϭ 0 63. y x ϩ ϭ1 a b and and 3x ϩ 2y Ϫ 6 ϭ 0 y x Ϫ ϭ1 a b In Exercises 64–65, find the point of intersection of the lines with the given equations. 35. A(Ϫ3, 6), B(3, 3), and C(6, 0) 38. y ϩ 4 ϭ 0 60. 3x Ϫ 4y ϭ 8 In Exercises 46–59, find an equation of the line satisfying the conditions. Write your answer in the slope-intercept form. 46. Is perpendicular to the x-axis and passes through the point (p, p2) 47. Passes through (4, Ϫ3) with slope 2 48.

Is perpendicular to the x-axis and passes through the point (p, p2) 47. Passes through (4, Ϫ3) with slope 2 48. Passes through (Ϫ3, 3) and has slope 0 49. Passes through (2, 4) and (3, 8) 50. Passes through (Ϫ1, Ϫ2) and (3, Ϫ4) 51. Passes through (2, 5) and (2, 28) 52. Has slope Ϫ2 and y-intercept 3 53. Has slope 3 and y-intercept Ϫ5 54. Has x-intercept 3 and y-intercept Ϫ5 55. Passes through (3, Ϫ5) and is parallel to the line with equation 2x ϩ 3y ϭ 12 56. Is perpendicular to the line with equation y ϭ Ϫ3x Ϫ 5 and has y-intercept 7 57.