Essential Calculus: Early Transcendentals
James Stewart
Language: English
Pages: 960
ISBN: 1133112285
Format: PDF / Kindle (mobi) / ePub
This book is for instructors who think that most calculus textbooks are too long. In writing the book, James Stewart asked himself: What is essential for a three-semester calculus course for scientists and engineers? ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS, Second Edition, offers a concise approach to teaching calculus that focuses on major concepts, and supports those concepts with precise definitions, patient explanations, and carefully graded problems. The book is only 900 pages--two-thirds the size of Stewart's other calculus texts, and yet it contains almost all of the same topics. The author achieved this relative brevity primarily by condensing the exposition and by putting some of the features on the book's website, www.StewartCalculus.com. Despite the more compact size, the book has a modern flavor, covering technology and incorporating material to promote conceptual understanding, though not as prominently as in Stewart's other books. ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS features the same attention to detail, eye for innovation, and meticulous accuracy that have made Stewart's textbooks the best-selling calculus texts in the world.
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ഛ 2, so the domain of t ؠt is the closed interval ͓Ϫ2, 2͔. ■ It is possible to take the composition of three or more functions. For instance, the composite function f ؠt ؠh is found by first applying h, then t, and then f as follows: ͑ f ؠt ؠh͒͑x͒ f ͑ t͑h͑x͒͒͒ So far we have used composition to build complicated functions from simpler ones. But in calculus it is often useful to be able to decompose a complicated function into simpler ones, as in the following example. EXAMPLE 6.
An equation for the family of linear functions with 0 A CATALOG OF ESSENTIAL FUNCTIONS x (1, _2.5) 5. Find an expression for a cubic function f if f ͑1͒ 6 and f ͑Ϫ1͒ f ͑0͒ f ͑2͒ 0. 6. Some scientists believe that the average surface temperature of the world has been rising steadily. They have modeled the temperature by the linear function T 0.02t ϩ 8.50, where T is temperature in ЊC and t represents years since 1900. (a) What do the slope and T -intercept represent? (b) Use the.
X≠0 (b) ƒ= ≈ 1 if x=0 0 x (c) ƒ= 1 2 x ≈-x-2 if x≠2 x-2 1 if x=2 0 1 2 3 (d) ƒ=[ x ] FIGURE 3 Graphs of the functions in Example 2 2 DEFINITION A function f is continuous from the right at a number a if lim f ͑x͒ f ͑a͒ x laϩ and f is continuous from the left at a if lim f ͑x͒ f ͑a͒ x laϪ x 48 ■ CHAPTER 1 FUNCTIONS AND LIMITS EXAMPLE 3 At each integer n, the function f ͑x͒ ͠x͡ [see Figure 3(d)] is continu- ous from the right but discontinuous from the left because.
Continuous on its domain. State ■ ■ the domain. sx 2 Ϫ 9 (a) t͑x͒ 2 x Ϫ2 ■ ■ ■ ■ ■ 4 (b) h͑x͒ s x ϩ x 3 cos x ■ Use the Intermediate Value Theorem to show that there is a root of the equation in the given interval. 49–50 50. 2 sin x 3 Ϫ 2x, ■ ■ x l0 49. 2x 3 ϩ x 2 ϩ 2 0, ■ ■ ͭ x l3 cos2 x x2 ■ ■ 2 ϱ sx Ϫ 4 (b) Where is f discontinuous? (c) Sketch the graph of f . 40. y sx 2 ϩ x ϩ 1 Ϫ sx 2 Ϫ x ■ ■ (a) Evaluate each limit, if it exists. (i) limϩ f ͑x͒ (ii) limϪ.
Is V 3 r 3. If the error 4 in the measured value of r is denoted by dr ⌬r, then the corresponding error in the calculated value of V is ⌬V, which can be approximated by the differential dV 4 r 2 dr When r 21 and dr 0.05, this becomes dV 4 ͑21͒2 0.05 Ϸ 277 The maximum error in the calculated volume is about 277 cm3. ■ NOTE Although the possible error in Example 3 may appear to be rather large, a better picture of the error is given by the relative error, which is computed by.