# Brief Calculus: An Applied Approach, 7th Edition by Ron Larson

By Ron Larson

Designed particularly for the non-math significant who should be utilizing calculus in company, economics, or lifestyles and social technological know-how classes, short Calculus: An utilized method, 7/e, addresses scholars' susceptible math talents via extra constitution and counsel on the best way to examine math. targeted student-success-oriented sections comprise chapter-opening innovations for fulfillment; What you'll want to Learn--and Why you'll want to research It; part pursuits; bankruptcy Summaries and examine options; try out Its; examine suggestions; and Warm-Up routines. moreover the textual content provides Algebra advice at aspect of use and Algebra evaluation on the finish of every bankruptcy.

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For instance, when you substitute x ϭ 1 into each expression, you obtain Ί2. 5 Fractions and Rationalization 0-31 Rationalization Techniques In working with quotients involving radicals, it is often convenient to move the radical expression from the denominator to the numerator, or vice versa. For example, you can move Ί2 from the denominator to the numerator in the following quotient by multiplying by Ί2͞Ί2. Radical in Denominator Rationalize Radical in Numerator 2 ΂ 2 2΃ 1 Ί2 1 Ί Ί2 Ί Ί 2 This process is called rationalizing the denominator.

3xΊx x 1͞2 28. x Ίx ΂ ΃ 3 12s 2 9s 3 31. (a) Ί8 (b) Ί18 3 16 32. (a) Ί 27 3 24 (b) Ί 125 3 16x 5 33. (a) Ί 4 32x 4 z 5 (b) Ί 4 ͑3x 2 y 3͒ 4 34. (a) Ί 3 54x 7 (b) Ί 3 144x 9 yϪ4 z 5 35. (a) Ί (b) Ί12͑3x ϩ 5͒7 4 32xy 5zϪ8 36. (a) Ί (b) Ί90͑2x Ϫ 3y͒6 In Exercises 37–46, simplify each expression by factoring. 37. 4x 3 Ϫ 6x 39. ϩ 50. Ί4x 2 ϩ 1 1 52. 3 x Ϫ 1 Ί Ίx ϩ 2 54. xϪ4 56. 1 3 x ϩ 4 Ί Ίx Ϫ 1 xϩ1 1 Ί2x ϩ 3 xϪ1͞2 ϩ Ί6 Ϫ 4x Compound Interest In Exercises 57–60, a certificate of ΂ AϭP 1ϩ r n ΃ N into a graphing utility and use it to find the balance after N compoundings.

14. 2x + 3 is not defined for these x. − 32 2x + 3 is defined for these x. 14 EXAMPLE 7 Finding the Domain of an Expression Find the domain of each expression. (a) Ί3x Ϫ 2 (b) 1 Ί3x Ϫ 2 3 9x ϩ 1 (c) Ί SOLUTION (a) The domain of Ί3x Ϫ 2 consists of all x such that 3x Ϫ 2 ≥ 0 which implies that x ≥ Expression must be nonnegative. 2 3. So, the domain is ͓3, ϱ͒. 2 (b) The domain of 1͞Ί3x Ϫ 2 is the same as the domain of Ί3x Ϫ 2, except that 1͞Ί3x Ϫ 2 is not defined when 3x Ϫ 2 ϭ 0. Because this occurs when x ϭ 23, the domain is ͑23, ϱ͒.