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Download Calculus: Concepts and Contexts (4th Edition) (Stewart's by James Stewart PDF

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By James Stewart

4th edition

Stewart's CALCULUS: suggestions AND CONTEXTS, FOURTH variation deals a streamlined method of instructing calculus, targeting significant suggestions and assisting people with unique definitions, sufferer factors, and punctiliously graded difficulties. CALCULUS: techniques AND CONTEXTS is very appeared simply because this article deals a stability of idea and conceptual paintings to fulfill extra revolutionary courses in addition to people who find themselves more well-off educating in a extra conventional model. each one identify is only one part in a complete calculus direction software that rigorously integrates and coordinates print, media, and expertise items for profitable educating and studying.

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Extra resources for Calculus: Concepts and Contexts (4th Edition) (Stewart's Calculus Series)

Example text

47. The line segment joining the points ͑1, Ϫ3͒ and ͑5, 7͒ 48. The line segment joining the points ͑Ϫ5, 10͒ and ͑7, Ϫ10͒ 49. The bottom half of the parabola x ϩ ͑ y Ϫ 1͒2 ෇ 0 50. The top half of the circle x 2 ϩ ͑ y Ϫ 2͒ 2 ෇ 4 f ͑3 ϩ h͒ Ϫ f ͑3͒ h 51. 52. y y f ͑a ϩ h͒ Ϫ f ͑a͒ h f ͑x͒ Ϫ f ͑a͒ xϪa xϩ3 28. f ͑x͒ ෇ , xϩ1 xϩ4 x2 Ϫ 9 3 31. f ͑t͒ ෇ s 2t Ϫ 1 1 1 0 f ͑x͒ Ϫ f ͑1͒ xϪ1 1 x 0 1 53–57 Find a formula for the described function and state its domain. 29–33 Find the domain of the function. 29. f ͑x͒ ෇ 47–52 Find an expression for the function whose graph is the 30.

Returning to the series in Equation 3, we denote by sn the sum of the first n terms of the series. 99998474 4 2 Observe that as we add more and more terms, the partial sums become closer and closer to 1. In fact, it can be shown that by taking n large enough (that is, by adding sufficiently many terms of the series), we can make the partial sum sn as close as we please to the number 1. It therefore seems reasonable to say that the sum of the infinite series is 1 and to write 1 1 1 1 ϩ ϩ ϩ иии ϩ n ϩ иии ෇ 1 2 4 8 2 10 A PREVIEW OF CALCULUS In other words, the reason the sum of the series is 1 is that lim sn ෇ 1 nlϱ In Chapter 8 we will discuss these ideas further.

Its graph is always a parabola obtained by shifting the parabola y ෇ ax 2, as we will see in the next section. The parabola opens upward if a Ͼ 0 and downward if a Ͻ 0. ) y y 2 2 x 1 0 FIGURE 7 The graphs of quadratic functions are parabolas. 1 x (b) y=_2≈+3x+1 (a) y=≈+x+1 A polynomial of degree 3 is of the form P͑x͒ ෇ ax 3 ϩ bx 2 ϩ cx ϩ d a 0 and is called a cubic function. Figure 8 shows the graph of a cubic function in part (a) and graphs of polynomials of degrees 4 and 5 in parts (b) and (c).

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