By Ron Larson
Designed in particular for company, economics, or life/social sciences majors, Calculus: An utilized strategy, 8/e, motivates scholars whereas fostering realizing and mastery. The booklet emphasizes built-in and fascinating purposes that convey scholars the real-world relevance of issues and ideas. a number of pedagogical features--from algebra assessment to check tips--provide additional suggestions and perform. The 8th version builds upon its purposes emphasis via up to date routines and correct examples. utilized difficulties drawn from govt resources, undefined, present occasions, and different disciplines supply well-rounded examples and attract diversified pursuits. moreover, the Calculus software bargains a robust help package--including MathSPACE Instructor/Student web content and path administration instruments, educational DVDs, and suggestions manuals--that permits scholars to check the fabric independently and continue key thoughts.
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Additional info for Calculus: An Applied Approach
A. x 2 Ϫ 5x ϩ 6 b. x 2 Ϫ 6x ϩ 9 c. 2x 2 ϩ 5x Ϫ 3 SOLUTION a. Because x 2 Ϫ 5x ϩ 6 ϭ ͑x Ϫ 2͒͑x Ϫ 3͒ STUDY TIP The zeros of a polynomial in x are the values of x that make the polynomial zero. To find the zeros, factor the polynomial into linear factors and set each factor equal to zero. For instance, the zeros of ͑x Ϫ 2͒͑x Ϫ 3͒ occur when x Ϫ 2 ϭ 0 and x Ϫ 3 ϭ 0. the zeros are x ϭ 2 and x ϭ 3. b. Because x 2 Ϫ 6x ϩ 9 ϭ ͑x Ϫ 3͒2 the only zero is x ϭ 3. c. Because 2x 2 ϩ 5x Ϫ 3 ϭ ͑2x Ϫ 1͒͑x ϩ 3͒ the zeros are x ϭ 12 and x ϭ Ϫ3.
8. 8177 33. Physiology The maximum heart rate of a person in normal health is related to the person’s age by the equation 9. 3 Ί 60 10. 2e In Exercises 11–14, determine whether each given value of x satisfies the inequality. 11. 5x Ϫ 12 > 0 (a) x ϭ 3 12. x ϩ 1 < (b) x ϭ Ϫ3 5 (c) x ϭ 2 (b) x ϭ 4 (c) x ϭ Ϫ4 x 3 (a) x ϭ 0 xϪ2 < 2 13. 0 < 4 (a) x ϭ 4 14. Ϫ1 < (b) x ϭ 10 (c) x ϭ 0 3Ϫx ≤ 1 2 (a) x ϭ 0 (b) x ϭ 1 (c) x ϭ 5 In Exercises 15–28, solve the inequality and sketch the graph of the solution on the real number line.
6. ✓CHECKPOINT 1 Find the solution set of the inequality 2x Ϫ 3 < 7. ■ In Example 1, all five inequalities listed as steps in the solution have the same solution set, and they are called equivalent inequalities. 1 The Real Number Line and Order 5 The inequality in Example 1 involves a first-degree polynomial. To solve inequalities involving polynomials of higher degree, you can use the fact that a polynomial can change signs only at its real zeros (the real numbers that make the polynomial zero).
Calculus: An Applied Approach by Ron Larson