Single Variable Calculus: Concepts and Contexts (Stewart's by James Stewart

By James Stewart

Stewart's CALCULUS: strategies AND CONTEXTS, FOURTH version deals a streamlined method of educating calculus, targeting significant strategies and assisting people with exact definitions, sufferer reasons, and thoroughly graded difficulties. CALCULUS: thoughts AND CONTEXTS is very appeared simply because this article bargains a stability of thought and conceptual paintings to meet extra revolutionary courses in addition to those who find themselves more well-off educating in a extra conventional model. every one identify is only one part in a accomplished calculus direction software that rigorously integrates and coordinates print, media, and expertise items for winning educating and studying.

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A) y ෇ Ϫf ͑x͒ (b) y ෇ 2 f ͑x͒ Ϫ 1 (c) y ෇ f ͑x Ϫ 3͒ ϩ 2 5. Without using a calculator, make a rough sketch of the graph. (a) y ෇ x 3 (d) y ෇ 4 Ϫ x 2 (g) y ෇ Ϫ2 x 6. Let f ͑x͒ ෇ (b) y ෇ ͑x ϩ 1͒3 (e) y ෇ sx (h) y ෇ 1 ϩ x Ϫ1 ͭ 1 Ϫ x2 2x ϩ 1 (c) y ෇ ͑x Ϫ 2͒3 ϩ 3 (f) y ෇ 2 sx if x ഛ 0 if x Ͼ 0 (a) Evaluate f ͑Ϫ2͒ and f ͑1͒. (b) Sketch the graph of f . 7. If f ͑x͒ ෇ x ϩ 2x Ϫ 1 and t͑x͒ ෇ 2x Ϫ 3, find each of the following functions. 2 (a) f ‫ ؠ‬t (b) t ‫ ؠ‬f (c) t ‫ ؠ‬t ‫ ؠ‬t Answers to Diagnostic Test C: Functions 1.

In what follows, we discuss the behavior and graphs of these functions and give examples of situations appropriately modeled by such functions. Linear Models The coordinate geometry of lines is reviewed in Appendix B. When we say that y is a linear function of x, we mean that the graph of the function is a line, so we can use the slope-intercept form of the equation of a line to write a formula for the function as y ෇ f ͑x͒ ෇ mx ϩ b where m is the slope of the line and b is the y-intercept. 26 CHAPTER 1 FUNCTIONS AND MODELS A characteristic feature of linear functions is that they grow at a constant rate.

Express the lengths a and b in the figure in terms of ␪. 24 6. If sin x ෇ 3 and sec y ෇ 4, where x and y lie between 0 and ␲ր 2, evaluate sin͑x ϩ y͒. 1 a 5 7. Prove the identities. ¨ (a) tan ␪ sin ␪ ϩ cos ␪ ෇ sec ␪ b FIGURE FOR PROBLEM 5 (b) 2 tan x ෇ sin 2x 1 ϩ tan 2x 8. Find all values of x such that sin 2x ෇ sin x and 0 ഛ x ഛ 2␲. 9. Sketch the graph of the function y ෇ 1 ϩ sin 2x without using a calculator. Answers to Diagnostic Test D: Functions 1. (a) 5␲͞3 (b) Ϫ␲͞10 6. 2. 6Њ 8. 0, ␲͞3, ␲, 5␲͞3, 2␲ 1 15 (4 ϩ 6 s2 ) 9.

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