Calculus: Concepts and Contexts (2nd Edition) by James Stewart

By James Stewart

James Stewart's well-received CALCULUS: ideas AND CONTEXTS, moment version follows within the course of the opposite best-selling books through this amazing writer. the 1st variation of this ebook used to be hugely profitable since it reconciled faculties of notion: it skillfully merged the simplest of conventional calculus with the easiest of the reform stream. This re-creation maintains to supply the balanced method in addition to Stewart's hallmark beneficial properties: meticulous accuracy, sufferer reasons, and thoroughly graded difficulties. The content material has been sophisticated and the examples and routines were up-to-date. moreover, CALCULUS: recommendations AND CONTEXTS, moment version now features a loose CD-ROM for college students that comprises animations, actions, and homework tricks. The publication integrates using the CD all through through the use of icons that convey scholars while to take advantage of the CD to deepen their figuring out of a tricky notion. In CALCULUS: suggestions AND CONTEXTS, this good revered writer emphasizes conceptual knowing - motivating scholars with actual international purposes and stressing the guideline of 4 in numerical, visible, algebraic, and verbal interpretations. All strategies are provided within the vintage Stewart kind: with simplicity, personality, and a spotlight to element. as well as his transparent exposition, Stewart additionally creates good thought-out difficulties and workouts. The definitions are distinctive and the issues create a great stability among conceptual knowing and algebraic talents.

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4 _4 1000 30 4 10 _10 _50 50 _4 _5 _100 (b) ͓_4, 4͔ by ͓_4, 4͔ (c) ͓_10, 10͔ by ͓_5, 30͔ (d) ͓_50, 50͔ by ͓_100, 1000͔ FIGURE 2 Graphs of ƒ=≈+3 We see from Example 1 that the choice of a viewing rectangle can make a big difference in the appearance of a graph. Sometimes it’s necessary to change to a larger viewing rectangle to obtain a more complete picture, a more global view, of the graph. In the next example we see that knowledge of the domain and range of a function sometimes provides us with enough information to select a good viewing rectangle.

We choose the viewing rectangle so that the x-interval is somewhat larger than the domain and the y-interval is larger than the range. Taking the viewing rectangle to be ͓Ϫ3, 3͔ by ͓Ϫ1, 4͔, we get the graph shown in Figure 3. EXAMPLE 3 Graph the function y ෇ x 3 Ϫ 150x. SOLUTION Here the domain is ‫ޒ‬, the set of all real numbers. That doesn’t help us 5 _5 5 _5 FIGURE 4 choose a viewing rectangle. Let’s experiment. If we start with the viewing rectangle ͓Ϫ5, 5͔ by ͓Ϫ5, 5͔, we get the graph in Figure 4.

To obtain the graph of y ෇ cf ͑x͒, stretch the graph of y ෇ f ͑x͒ vertically by a factor of c y ෇ ͑1͞c͒f ͑x͒, compress the graph of y ෇ f ͑x͒ vertically by a factor of c y ෇ f ͑cx͒, compress the graph of y ෇ f ͑x͒ horizontally by a factor of c y ෇ f ͑x͞c͒, stretch the graph of y ෇ f ͑x͒ horizontally by a factor of c y ෇ Ϫf ͑x͒, reflect the graph of y ෇ f ͑x͒ about the x-axis y ෇ f ͑Ϫx͒, reflect the graph of y ෇ f ͑x͒ about the y-axis Figure 3 illustrates these stretching transformations when applied to the cosine function with c ෇ 2.

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