Calculus: An Applied Approach by Ron Larson

By Ron Larson

Designed in particular for company, economics, or life/social sciences majors, CALCULUS: AN utilized procedure, short, 10th version, motivates scholars whereas fostering knowing and mastery. The publication emphasizes built-in and interesting functions that express scholars the real-world relevance of subject matters and ideas. utilized difficulties drawn from executive resources, undefined, present occasions, and different disciplines supply well-rounded examples and attract scholars' diversified pursuits. The 10th version builds upon its functions emphasis via up to date routines and correct examples. Pedagogical features--from algebra evaluation to check tips--continue to supply additional assistance and perform. furthermore, the recent version is now supported via powerful non-compulsory electronic studying options, greater WebAssign and MindTap Math, and stepped-out answer video clips with guideline can be found at CalcView.com for chosen routines through the textual content.

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TECHNOLOGY > A graphing utility offers several ways to calculate rational exponents and radicals. You should be familiar with the x-squared key x 2 . This key squares the value of an expression. For rational exponents or exponents other than 2, use the key. For radical expressions, you can use the square root key Ί , the cube root key Ί3 , or the xth root key Ίx . Consult your graphing utility user’s guide for specific keystrokes you can use to evaluate rational exponents and radical expressions.

4 b. In this case, a ϭ 1, b ϭ 6, and c ϭ 9, and the Quadratic Formula yields xϭ Ϫb ± Ίb 2 Ϫ 4ac Ϫ6 ± Ί36 Ϫ 36 6 ϭ ϭ Ϫ ϭ Ϫ3. 2a 2 2 So, there is one (repeated) real zero: x ϭ Ϫ3. c. For this quadratic equation, a ϭ 2, b ϭ Ϫ6, and c ϭ 5. So, xϭ Ϫb ± Ίb 2 Ϫ 4ac 6 ± Ί36 Ϫ 40 6 ± ΊϪ4 . ϭ ϭ 2a 4 4 Because ΊϪ4 is imaginary, there are no real zeros. ✓CHECKPOINT 1 Use the Quadratic Formula to find all real zeros of each polynomial. a. 2x2 ϩ 4x ϩ 1 b. x2 Ϫ 8x ϩ 16 c. 2x2 Ϫ x ϩ 5 ■ The zeros in Example 1(a) are irrational, and the zeros in Example 1(c) are imaginary.

For rational exponents or exponents other than 2, use the key. For radical expressions, you can use the square root key Ί , the cube root key Ί3 , or the xth root key Ίx . Consult your graphing utility user’s guide for specific keystrokes you can use to evaluate rational exponents and radical expressions. Use a graphing utility to evaluate each expression. a. ͑Ϫ8͒2͞3 b. ͑16 Ϫ 5͒ 4 c. Ί576 3 729 d. Ί Example 6 Simplify each expression by factoring. a. b. ■ x 3 3 ͑x ϩ 1͒ 5͞3 ϩ ͑x ϩ 1͒ 8͞3 5 4 e. 3͑x ϩ 2͒ 2͑x Ϫ 1͒ 3 Ϫ 3͑x ϩ 2͒ 3͑x Ϫ 1͒ 2 ͓͑x Ϫ 1͒ 3͔ 2 SOLUTION a.

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