Download Calculus: One and Several Variables, 10th Edition by Saturnino L. Salas; Garret J. Etgen; Einar Hille; PDF

By Saturnino L. Salas; Garret J. Etgen; Einar Hille;

For ten versions, readers have grew to become to Salas to profit the tricky suggestions of calculus with out sacrificing rigor. The publication regularly presents transparent calculus content material to aid them grasp those innovations and comprehend its relevance to the genuine global. through the pages, it deals an ideal stability of concept and purposes to raise their mathematical insights. Readers also will locate that the e-book emphasizes either problem-solving abilities and real-world functions.

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Exercises 21–24. Write an equation for the line with 21. slope 5 and y-intercept 2. 22. slope 5 and y-intercept −2. 23. slope −5 and y-intercept 2. 24. slope −5 and y-intercept −2. Exercises 25–26. Write an equation for the horizontal line 3 units 25. above the x-axis. 26. below the x-axis. Exercises 27–28. Write an equation for the vertical line 3 units 27. to the left of the y-axis. 28. to the right of the y-axis. Exercises 29–34. Find an equation for the line that passes through the point P(2, 7) and is 29.

X − 12 | < 2. 25. |x − 2| < 12 . 27. 0 < |x| < 1. 28. 0 < |x| < 12 . 29. 0 < |x − 2| < 12 . 30. 0 < |x − 12 | < 2. 31. 0 < |x − 3| < 8. 32. |3x − 5| < 3. 1 34. |5x − 3| < 12 . 33. |2x + 1| < 4 . 35. |2x + 5| > 3. 36. |3x + 1| > 5. Exercises 37–42. Each of the following sets is the solution of an inequality of the form | x − c |< δ. Find c and δ. 4 COORDINATE PLANE; ANALYTIC GEOMETRY 37. (−3, 3). 38. (−2, 2). 39. (−3, 7). 40. (0, 4). 41. (−7, 3). 42. (a, b). Exercises 43–46. Determine all numbers A > 0 for which the statement is true.

SOLUTION The slope of l1 is 3 4 and the slope of l2 is 12 . 5 Since l1 and l2 have different slopes, they intersect at a point. To find the point of intersection, we solve the two equations simultaneously: 3x − 4y + 8 = 0 12x − 5y − 12 = 0. Multiplying the first equation by −4 and adding it to the second equation, we obtain 11y − 44 = 0 y = 4. Substituting y = 4 into either of the two given equations, we find that x = 83 . The lines intersect at the point ( 83 , 4). 1. The information we give here suffices for our present purposes.

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