By James Stewart
Luck on your calculus path begins right here! James Stewart's Calculus texts are world wide best-sellers for a cause: they're transparent, exact, and packed with suitable, real-world examples. With Calculus (Seventh Edition), Stewart conveys not just the software of calculus that can assist you advance technical competence, but in addition provides an appreciation for the intrinsic great thing about the topic. His sufferer examples and integrated studying aids can assist you construct your mathematical self belief and accomplish your pursuits within the path!
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Extra info for Calculus (7th Edition)
SOLUTION Remember that a function is a rule. For this particular function the rule is the following: First look at the value of the input x. If it happens that x ഛ Ϫ1, then the value of f ͑x͒ is 1 Ϫ x. On the other hand, if x Ͼ Ϫ1, then the value of f ͑x͒ is x 2. Since Ϫ2 ഛ Ϫ1, we have f ͑Ϫ2͒ 1 Ϫ ͑Ϫ2͒ 3. Since Ϫ1 ഛ Ϫ1, we have f ͑Ϫ1͒ 1 Ϫ ͑Ϫ1͒ 2. y Since 0 Ͼ Ϫ1, we have f ͑0͒ 0 2 0. 1 _1 0 1 x FIGURE 15 How do we draw the graph of f ? We observe that if x ഛ Ϫ1, then f ͑x͒ 1 Ϫ x, so the part of the graph of f that lies to the left of the vertical line x Ϫ1 must coincide with the line y 1 Ϫ x, which has slope Ϫ1 and y-intercept 1.
Rewrite by completing the square. (a) x 2 ϩ x ϩ 1 (b) 2x 2 Ϫ 12x ϩ 11 8. Solve the equation. ) 2x Ϫ 1 2x xϩ1 x (d) 2x 2 ϩ 4x ϩ 1 0 (a) x ϩ 5 14 Ϫ 2 x 1 (b) (c) x2 Ϫ x Ϫ 12 0 Խ (e) x 4 Ϫ 3x 2 ϩ 2 0 (g) 2x͑4 Ϫ x͒Ϫ1͞2 Ϫ 3 s4 Ϫ x 0 Խ (f ) 3 x Ϫ 4 10 9. Solve each inequality. Write your answer using interval notation. (a) Ϫ4 Ͻ 5 Ϫ 3x ഛ 17 (c) x͑x Ϫ 1͒͑x ϩ 2͒ Ͼ 0 2x Ϫ 3 (e) ഛ1 xϩ1 (b) x 2 Ͻ 2x ϩ 8 (d) x Ϫ 4 Ͻ 3 Խ Խ 10. State whether each equation is true or false. (a) ͑ p ϩ q͒2 p 2 ϩ q 2 (b) sab sa sb (c) sa 2 ϩ b 2 a ϩ b (d) 1 ϩ TC 1ϩT C (f ) 1͞x 1 a͞x Ϫ b͞x aϪb (e) 1 1 1 Ϫ xϪy x y Answers to Diagnostic Test A: Algebra 1.
1 Exercises 1. If f ͑x͒ x ϩ s2 Ϫ x and t͑u͒ u ϩ s2 Ϫ u , is it true that f t? 2. If f ͑x͒ x2 Ϫ x xϪ1 and (c) (d) (e) (f) Estimate the solution of the equation f ͑x͒ Ϫ1. On what interval is f decreasing? State the domain and range of f. State the domain and range of t. t͑x͒ x is it true that f t? y g f 3. The graph of a function f is given. (a) (b) (c) (d) (e) (f) whenever x 1 Ͻ x 2 in I State the value of f ͑1͒. Estimate the value of f ͑Ϫ1͒. For what values of x is f ͑x͒ 1? Estimate the value of x such that f ͑x͒ 0.