several stocks and their rates of return

... Law of Cooling (Newton), 326, 985–986, 1002–1004, 1025–1028 Law of Cosines explanation of, 658–659, 709 proof of, 660–661 use of, 661–662 Law of Sines explanation of, 659–660, 709 proof of, 664 ... Test for convergence of series, 1129–1131 explanation of, 965–968, 977 proof of, 968 use of, 968–969, 972 Integrands antiderivative of, 805–806 definition of, 783 explanation of, 729, 770 expressed ... explanation of, 903 infinite interval of integration and, 903–907 method of comparison and, 912–914 methods to approach, 908–912 unbounded and discontinuous integrands and, 907–908 use of, 903 Increasing...

Ngày tải lên: 05/07/2014, 18:20

... set of problem-solving skills, and strengthening the students as learners of mathematics and science An integrated course offers freedom, new possibilities, and an invigorating freshness of outlook ... structure of this text is intended to facilitate learning deductive and inductive reasoning, learning to use examples and counterexamples, and learning to understand the usefulness of a variety of perspectives ... function and its derivative without being formally introduced to the derivative Part II focuses on rates of change and modeling using linear and quadratic functions Linearity and interpretation of...

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... Functions and Their Graphs N 373 391 EXPLORATORY PROBLEMS FOR CHAPTER 11: Functions and Their Graphs: Tinkering with Polynomials and Rational Functions 404 11.4 Rational Functions and Their Graphs ... Limits—Methods of Inquiry and a Definition 245 Left- and Right-Handed Limits; Sometimes the Approach Is Critical 7.3 7.4 N CHAPTER 226 A Streetwise Approach to Limits 265 Continuity and the Intermediate and ... Basic Vocabulary and Notation 1.3 CHAPTER Functions Are Everywhere N 1.2 Representations of Functions 15 Characterizing Functions and Introducing Rates of Change 49 2.1 Features of a Function:...

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... temperature and the pressure of a gas, an environmental scientist in the relationship between use of pesticides and mortality rate of songbirds, a physician in the relationship between the radius of a ... about it, think of the set of parentheses ( ) as a pair of hands cupped to receive the input The output spurts out of the equal sign 1.2 What Are Functions? Basic Vocabulary and Notation Definition ... expression y = f (x) is shorthand for “y is the output of f corresponding to an input of x” and it is read “y equals f of x.” When we say y = f (x), we mean that y depends on x and is uniquely determined...

Ngày tải lên: 05/07/2014, 18:20

... is the set of all acceptable volumes: [0, B], where B is the volume of the full beaker The volume of a cylinder of height h and radius r is the product of the height and the area of the disk ... 0.04x The graphs of the functions f and g are given below What is the significance of the x-coordinate of the point of intersection of the lines? tax g 500 f cost of car Figure 1.4 REMARKS i The function ... the area of the circle and the function whose input is the radius of a circle and whose output is the area Recall that a “T” sign may sometimes be a landmark indicating a subway station and other...

Ngày tải lên: 05/07/2014, 18:20

... pounds of sugar cane with pounds of panda Question: How many calories does the panda need for one day? C calories · x lbs of panda = Cx calories lbs of panda Question: How many pounds of sugar ... We can use the volume of a cone to relate the amount of liquid, V , and the height, h, of the liquid V = π r 2h Here r is the radius of the top of the cone of liquid, not of the conical filter ... number of pounds of sugar cane it takes to support a pair of pandas, one weighing P pounds and the other weighing Q pounds, for a period of W weeks is a function of 1.3 Representations of Functions...

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... length of the sides of the base and let h denote the height of the box, s and h in inches (a) Express the volume of the box in terms of s and h (b) Express the surface area of the box in terms of ... function of s, the length of the side of the base 30 A rectangle is inscribed in a semicircle of radius R, where R is constant (a) Express the area of the rectangle as a function of the height, h, of ... function of time t, t in seconds 26 Express the area of a circle as a function of: (a) its diameter, d (b) its circumference, c 27 Express the surface area of a cube as a function of the length s of...

Ngày tải lên: 05/07/2014, 18:20

... of the archway by w and the height of the vertical wall of the rectangle y The width and height are given in meters (a) Express y, the height of the side wall, as a function of w, the width of ... typing and a flat rate of $10 per picture The cost of getting a document typed is a function of its length and the number of pictures Write a function that gives a good estimate of the cost of getting ... center row of yellow tulips Each row of flowers extends from one side of the plot to the other Express the length of a row of flowers as a function of its distance from the center line of yellow...

Ngày tải lên: 05/07/2014, 18:20

... we return to the four functions we introduced at the beginning of this section: f (x) = x, g(x) = x 2, h(x) = |x|, and j (x) = x (a) Which of functions f , g, h, and j are even? (b) Which of ... Characterizing Functions and Introducing Rates of Change Definition A is inversely proportional to B if A= k B for some constant k As B increases A decreases, and vice versa This type of relationship ... EXERCISE 2.5 Look at each of the functions f (x) = x, g(x) = x 2, h(x) = |x|, and j (x) = and answer the following questions x one by one (a) What are the domain and range of the function? (b) Where...

Ngày tải lên: 05/07/2014, 18:20

... Characterizing Functions and Introducing Rates of Change (a) The increase in the price of a cup of coffee in Seattle from 1970 to 2000 (b) The percent increase in the price of a cup of coffee in Seattle ... h(t) denote the height of a rocketship t seconds after takeoff (a) Express the average rate of change of height of the rocket betweeen and 2.01 seconds after takeoff in terms of the function h (b) ... is measured in seconds, amount of water in liters, and height of the water in centimeters Time Amount of Water Height of Water 0 1.5 4 The average rate of change of volume with respect to time...

Ngày tải lên: 05/07/2014, 18:20

... ratio of integers The decimal expansion of an irrational number is infinite and nonrepeating Some √ √ examples of irrational numbers are π, 2, and 5.14 The set of real numbers is the set of all ... amount functions and their corresponding rate functions EXERCISE 2.10 Oil is leaking from a point and spreading evenly in a thin, expanding disk We can measure the radius of the disk and want to know ... infinitely many of them Let’s return to our function f If we try to graph f , the best we can is along the lines of the figure below The domain of this function is the set of all real numbers, and the...

Ngày tải lên: 05/07/2014, 18:20

... Functions and Introducing Rates of Change (a) Describe the trip in words Include where the trip started and ended and how fast (and in what direction) we traveled (b) Graph velocity as a function of ... Inc 1997 17 Due in part to their methods of record keeping and their hot dry climate, the ancient Egyptians and Babylonians have left modern historians more evidence of their mathematical development ... Functions and Introducing Rates of Change death one of their members who revealed to the outside world this dreadful contradiction in beliefs.23 While rational numbers (positive, zero, and negative)...

Ngày tải lên: 05/07/2014, 18:20

... quotient of the functions I and P If h(x) = f (x) · g(x), then the output of h is the product of the outputs of f and g If j (x) = f (x) , then the output of j is the quotient of the outputs of f and ... sum of functions f and g, h(x) = f (x) + g(x), then the output of h corresponding to an input of x1 is the sum of f (x1) and g(x1) In terms of the graphs, the height of h at x1 is the sum of the ... heights of the graphs of f and g at x1 An analogous statement can be made for subtraction The domain of h is the set of all x common to the domains of both f and g N EXAMPLE 3.2 Let f (x) = x and...

Ngày tải lên: 05/07/2014, 18:20

... (fg)(x), and domains f g (x), and find their 39 f (x) = ax + b and g(x) = cx + d 40 f (x) = 3x + and g(x) = 5x − 41 f (x) = 2x + and g(x) = x − 42 f (x) = 43 f (x) = x+1 √ and g(x) = x and g(x) ... x- and y-intercepts of f (x) and g(x) affect the intercepts of f (x)g(x)? State this as a general rule 17 For what values of x (if any) is f (x) g(x) undefined? 18 How the x- and y-intercepts of ... Composition of Functions 113 iii Once we know A as a function of r and know r as a function of t we can find A as a function of t using composition of functions A(t) = π t, so each hour the area of the...

Ngày tải lên: 05/07/2014, 18:20

... How does the graph of y = cf (x) + k (where c and k are constants) relate to that of y = f (x)? In particular, let f (x) = x On the same set of axes sketch the graphs of f (x) and h(x), where h(x) ... −1, and −1 < k < i What is the effect on the x-intercepts? ii Do the locations of the peaks and valleys change? iii Do the heights of the peaks and valleys change? Alterations to both input and ... innermost part and remember the order of operations rules (b) Let q(x) = − x−4 + Interpret the graph of q in terms of transformations of a familiar function Where are the vertical and horizontal...

Ngày tải lên: 05/07/2014, 18:20

... with the graph of a familiar function and applying appropriate shifts, flips, and stretches Label all x- and y-intercepts and the coordinates of any vertices and corners Use exact values, not numerical ... rate of change of the function h over the interval [6, + h] ii One of the functions f , g, and h has an average value of −10 on the interval [6, + h] Which is it? Explain briefly P A R T II C H Rates ... x-coordinate of point A is and the x-coordinate of point B is (6 + h) Write mathematical expressions, using functional notation, for each of the following (a) The change in value of the function...

Ngày tải lên: 05/07/2014, 18:20

... examples of the use of local linearity arise in the fields of finance and economics Investors lay billions of dollars on the line when they use economic data to project into the future The question of ... rate of change of D = = 60 miles per hour N Definition f is a linear function of x if f can be written in the form f (x) = mx + b, where m and b are constants The graph of a linear function of ... line lies on the graph of the equation As discussed in Chapter 1, this is what it means to be the graph of a function The following are examples of equations of lines and their graphs f x –1 Figure...

Ngày tải lên: 05/07/2014, 18:20

... between the price of an item and the number of items demanded by consumers Below is a demand curve for a certain good q is the quantity of the good demanded (i.e., the number of items demanded) p is ... curve Let R = the number of units of item and S = the number of units of item S c a R (a) Write an equation for the line in terms of S, R, a, and c (b) Interpret the meanings of the intercepts (c) ... x-coordinates of P and Q are x = b and x = b + h (h = 0), respectively 16 f (x) = ax + bx + c; the x-coordinates of P and Q are x = k and x = k + h (h = 0), respectively 17 There is a proliferation of telephone-call...

Ngày tải lên: 05/07/2014, 18:20

... the value of x.) Inflation in Turkey has caused prices of small everyday items to be measured in tens of thousands of lira One day I went to a market and purchased one container of yogurt and two ... high-risk stocks and 40% into low-growth stocks If a client has $2 million invested in high-risk stocks and $3 million in low-risk stocks, how much of the client’s money is in option C and how ... the equation of the supply and demand curves shown in the figure below (b) What are the equilibrium price and quantity? Assume price is measured in dollars and quantity in thousands of units (The...

Ngày tải lên: 05/07/2014, 18:20

... from a height of 256 ft and given no initial velocity |h| is a handy notation for “the size of h” or “the magnitude of h.” 5.1 Calculating the Slope of a Curve and Instantaneous Rate of Change 175 ... definition of the derivative of f (c) f (c) is called the derivative of f at x = c We read f (c) aloud as “f prime of c.” f (c) can be interpreted as the rate of change of f at x = c or as the slope of ... instantaneous rate of change of f at x = a can be approximated by the average rate of change of f on [a, a + h] for h very close to zero As h gets closer and closer to zero, the average rate of change...

Ngày tải lên: 05/07/2014, 18:20