By Jerrold Marsden, Alan Weinstein
Undergraduate Texts in arithmetic
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Additional resources for Calculus I (Undergraduate Texts in Mathematics)
8. k2+4\ + +I 5 2). 232 Example 8 Solution (a) Where does the line y = 3x + 4 intersect the parabola y (b) For which values of x is 8x2 < 3x + 4? (a) We solve these equations simultaneously: -3x+y-4=0, y = 8x2. Substituting the second equation into the first gives - 3x 8x2-3x-4-0. 9. The line y = 3 x 4 intersects the parabola y = 8x2at two points. + = 8x2? 544. 74. 37). (See Fig. x + y - 4 = 0. If the final quadratic equation had just one root-a double root-there would have been just one point of intersection; if no (real) roots, then no points of intersection.
31. ( 2 x - 5 ) ( x - 3 ) > O o r x E ( - 5 1 1 , butnot both. 32. (x - 3)(3x - 10) < 0 and x2(5x - 15) > 0. Simplify the expressions in Exercises 33-36. 33. / - 81 5 34. ( ( a + 112-2a- 11 35. 110 - (6 12)l 36. 1 - 181 + I - 21 Simplify the expressions in Exercises 37-44. 37. 0 . 2- + + + 50. ( - 1,6),(1, -6) 51. (-2,3),(1,0) 52. (5,5),(-3, -2) Find the equation of the line passing through the given point P with slope rn in Exercises 53-56. 13), m = - 3 53. P = (i, 54. P = (15, - l), rn = 9 55.
Copyright 1985 Springer-Verlag. All rights reserved. 42 Chapter Fa Review of Fundamentals Example 4 Solution Draw the graph of f ( x ) = 3x2. 5). A 'C = 3x2, drawn in Fig. 3 (see Exampk 5 Let g be the absolute value function defined by g ( x ) = 1x1. ) Draw the graph of g. Solution We begin by choosing various values of x in the domain, computing g(x), and plotting the points ( x , g(x)). Connecting these points results in the graph shown in Fig. 4. Another approach is to use the definition We observe that the part of the graph of g for x > 0 is a line through (0,0) with slope 1 , while the part for x < 0 is a line through (0,O) with slope - 1.
Calculus I (Undergraduate Texts in Mathematics) by Jerrold Marsden, Alan Weinstein