By Ron Larson, Bruce H. Edwards
CALCULUS OF A unmarried VARIABLE: EARLY TRANSCENDENTAL capabilities, 6th version, deals scholars leading edge studying assets. each variation from the 1st to the 6th of CALCULUS: EARLY TRANSCENDENTAL features has made the mastery of conventional calculus abilities a concern, whereas embracing the simplest positive factors of recent expertise and, while acceptable, calculus reform rules.
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Extra resources for Calculus of a Single Variable: Early Transcendental Functions
In Exercises 21–26, find the domain of the function. (b) Identify f ͧ؊2ͨ and gͧ3ͨ. (d) Estimate the solution(s) of f ͧxͨ ؍2. 2 1 Ϫ cos x 24. h͑x͒ ϭ 25. f ͑x͒ ϭ 1 x ϩ Խ 3Խ 26. g͑x͒ ϭ 2 x −4 4 −2 4 f 2 g x −4 2 −2 4 −4 In Exercises 3–12, evaluate (if possible) the function at the given value(s) of the independent variable. Simplify the results. (a) f ͑0͒ 4. f ͑x͒ ϭ Ίx ϩ 5 (a) f ͑Ϫ4͒ (b) f ͑Ϫ3͒ (b) f ͑11͒ (c) f ͑b͒ (c) f ͑Ϫ8͒ (d) f ͑x Ϫ 1͒ 5. g͑x͒ ϭ 5 Ϫ x2 ͑x Ϫ 4͒ x2 (a) g͑4͒ (c) g͑Ϫ2͒ (c) g͑c͒ (d) g͑t Ϫ 1͒ (d) g͑t ϩ 4͒ (b) g͑Ί5 ͒ 7.
If the x- and y-axes have the same unit of measure, the slope has no units and is a ratio. If the x- and y-axes have different units of measure, the slope is a rate or rate of change. In your study of calculus, you will encounter applications involving both interpretations of slope. Population (in millions) EXAMPLE 2 Population Growth and Engineering Design 6 a. The population of Colorado was 3,827,000 in 1995 and 4,665,000 in 2005. 16 ϭ 83,800 people per year. 16). S. Census Bureau) b. 17. The slope of the ski ramp is the ratio of its height (the rise) to the length of its base (the run).
A) Write a linear equation giving the value y of the equipment in terms of the time x, 0 Յ x Յ 5. (b) Find the value of the equipment when x ϭ 2. (c) Estimate (to two-decimal-place accuracy) the time when the value of the equipment is $200. 83. Apartment Rental A real estate office manages an apartment complex with 50 units. When the rent is $780 per month, all 50 units are occupied. However, when the rent is $825, the average number of occupied units drops to 47. Assume that the relationship between the monthly rent p and the demand x is linear.