By Ron Larson
Designed particularly for company, economics, or life/social sciences majors, Calculus: An utilized strategy, 8/e, motivates scholars whereas fostering figuring out and mastery. The e-book emphasizes built-in and fascinating purposes that convey scholars the real-world relevance of issues and ideas. a number of pedagogical features--from algebra evaluation to review tips--provide additional tips and perform. The 8th version builds upon its functions emphasis via up-to-date routines and suitable examples. utilized difficulties drawn from executive assets, undefined, present occasions, and different disciplines supply well-rounded examples and entice various pursuits. moreover, the Calculus application deals a robust aid package--including MathSPACE Instructor/Student web content and path administration instruments, tutorial DVDs, and recommendations manuals--that permits scholars to study the cloth independently and continue key options.
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Extra resources for Calculus: An Applied Approach
09 12 x n x m ϭ x nϩm 1. Multiplying like bases: xn 2. 09 12 Subtract exponents. ͑xy͒n ϭ x n y n x n xn ϭ n y y n m ͑x ͒ ϭ x nm 3. Removing parentheses: 12 и 6 and 1200 ϭ x nϪm Add exponents. 12 и 6 Ϫx n ϭ Ϫ ͑x n͒, Ϫx n ͑Ϫx͒n cx n ϭ c͑x n͒, cx n ͑cx͒n m m m x n ϭ x͑n ͒, x n ͑x n͒m 4. * Example 3 Simplifying Expressions with Exponents Simplify each expression. a. 2x 2͑x 3͒ 3 x b. ͑3x͒ 2Ί c. 3x2 ͑x 1͞2͒3 5x4 ͑x2͒3 e. xϪ1͑2x 2͒ f. Ϫ Ίx 5xϪ1 d. SOLUTION a. 2x 2͑x 3͒ ϭ 2x 2ϩ3 ϭ 2x 5 x n x m ϭ x nϩm 3 x ϭ 9x 2x 1͞3 ϭ 9x 2ϩ ͑1͞3͒ ϭ 9x 7͞3 b.
The least common denominator is ͑x ϩ 2͒͑x Ϫ 3͒͑x ϩ 4͒. A B C ϩ ϩ xϩ2 xϪ3 xϩ4 A͑x Ϫ 3͒͑x ϩ 4͒ ϩ B͑x ϩ 2͒͑x ϩ 4͒ ϩ C͑x ϩ 2͒͑x Ϫ 3͒ ϭ ͑x ϩ 2͒͑x Ϫ 3͒͑x ϩ 4͒ 2 A͑x ϩ x Ϫ 12͒ ϩ B͑x 2 ϩ 6x ϩ 8͒ ϩ C͑x 2 Ϫ x Ϫ 6͒ ϭ ͑x ϩ 2͒͑x Ϫ 3͒͑x ϩ 4͒ 2 2 Ax ϩ Bx ϩ Cx 2 ϩ Ax ϩ 6Bx Ϫ Cx Ϫ 12A ϩ 8B Ϫ 6C ϭ ͑x ϩ 2͒͑x Ϫ 3͒͑x ϩ 4͒ 2 ͑A ϩ B ϩ C͒x ϩ ͑A ϩ 6B Ϫ C͒ x ϩ ͑Ϫ12A ϩ 8B Ϫ 6C͒ ϭ ͑x ϩ 2͒͑x Ϫ 3͒͑x ϩ 4͒ b. Here the least common denominator is ͑x ϩ 2͒ 2 ͑x Ϫ 1͒. A B C ϩ ϩ 2 x ϩ 2 ͑x ϩ 2͒ xϪ1 A͑x ϩ 2͒͑x Ϫ 1͒ ϩ B͑x Ϫ 1͒ ϩ C͑x ϩ 2͒ 2 ϭ ͑x ϩ 2͒ 2͑x Ϫ 1͒ A͑x 2 ϩ x Ϫ 2͒ ϩ B͑x Ϫ 1͒ ϩ C͑x 2 ϩ 4x ϩ 4͒ ϭ ͑x ϩ 2͒ 2͑x Ϫ 1͒ Ax 2 ϩ Cx 2 ϩ Ax ϩ Bx ϩ 4Cx Ϫ 2A Ϫ B ϩ 4C ϭ ͑x ϩ 2͒ 2͑x Ϫ 1͒ ͑A ϩ C͒x 2 ϩ ͑A ϩ B ϩ 4C͒x ϩ ͑Ϫ2A Ϫ B ϩ 4C͒ ϭ ͑x ϩ 2͒ 2͑x Ϫ 1͒ ✓CHECKPOINT 3 Perform each indicated addition of rational expressions.
In Exercises 1–20, evaluate the expression for the given value of x. Expression x-Value Expression 2 43. x-Value 44. ͑x 4 ϩ 2͒3͑x ϩ 3͒Ϫ1͞2 ϩ 4x 3͑x 4 ϩ 2͒2͑x ϩ 3͒1͞2 In Exercises 45–52, find the domain of the given expression. 1. Ϫ2x 3 xϭ3 2. x 3 xϭ6 3. 4xϪ3 xϭ2 4. 7xϪ2 xϭ5 1 ϩ xϪ1 5. xϪ1 xϭ3 6. x Ϫ 4x xϭ3 47. 7. 3x 2 Ϫ 4x 3 x ϭ Ϫ2 8. 5͑Ϫx͒ 3 xϭ3 49. 1 ͑Ϫx͒Ϫ3 xϭ4 9. 6x 0 Ϫ ͑6x͒0 x ϭ 10 Ϫ2 10. 3 x2 11. Ί x ϭ 27 12. Ίx 3 x ϭ 19 13. xϪ1͞2 xϭ4 14. xϪ3͞4 x ϭ 16 15. xϪ2͞5 x ϭ Ϫ32 16. ͑x2͞3͒3 x ϭ 10 17.