By Dale Varberg, Edwin J. Purcell, Steven E. Rigdon, Kevin M. Bodden
This the shortest mainstream calculus publication on hand. The authors make powerful use of computing expertise, pix, and functions, and supply no less than know-how tasks in step with bankruptcy. This well known booklet is right with no being excessively rigorous, up to date with no being faddish. keeps a robust geometric and conceptual concentration. Emphasizes rationalization instead of designated proofs. offers definitions regularly all through to take care of a transparent conceptual framework. offers enormous quantities of recent difficulties, together with difficulties on approximations, services outlined by way of tables, and conceptual questions. excellent for readers getting ready for the AP Calculus examination or who are looking to brush up on their calculus with a no-nonsense, concisely written booklet.
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Extra resources for Calculus: Student Solutions Manual (8th Edition)
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: Student Solutions Manual (8th Edition) by Dale Varberg, Edwin J. Purcell, Steven E. Rigdon, Kevin M. Bodden