... left blank Chapter CLIMATE CHANGE: ANINTEGRATEDPERSPECTIVE P Martens and J Rotmans 1.1 Introduction The consequences of rapid and substantial human-induced global climatechange on life on Earth ... time? Climate Change: AnIntegratedPerspective What drives processes such as urbanisation and migration? As indicated above, exploring global climatechange and its consequences for human society ... perspective to analyse and understand the complexity of the climate phenomenon We are convinced that anintegratedperspective can provide a useful guide to the problem of global climate change, and complement...
... Tanaka, 2006 Climate Change: What it Means for Us, Our Children, and Our Grandchildren, ed Joseph F.C DiMento, Pamela M Doughman, 2007 Creating a Climate for Change: Communicating ClimateChange ... Technology, Daniel Lashof, NRDC as published in Creating a Climate for Change, 2007 Climate Change: What It Means for Us, Our Children, and Our Grandchildren, Joseph F.C DiMento, and Pamela Doughman, ... Shelley Tanaka, 2006 Climate Change: What it Means for Us, Our Children, and Our Grandchildren, Joseph F.C DiMento, and Pamela Doughman, 2007 An Inconvenient Truth, Al Gore, 2006, http://www.pewclimate.org/global-warmingbasics/basic_science,...
... Conway, Kenneth Keniston, and the many participants in the MIT faculty workshops on "Humanistic Perspectives on Atmospheric Change" and "The Humanities and the Environment" that ran from 1991 to 1995 ... left blank Historical Perspectives on ClimateChange This page intentionally left blank Introduction Apprehending ClimateChange This most excellent canopy, the air, look you, this brave o'erhanging ... and changes and rates of change of environmental variables It poses new kinds of interdisciplinary viii PREFACE questions and proffers new types of answers At its best it challenges us to change...
... AnIntegrated Approach to Functions and Their Rates of Change P R E L I M I N A R Y E D I T I O N ROBIN J GOTTLIEB H A R V A R D U N I V E R S I T Y Sponsoring Editor: Laurie Rosatone Managing ... Ellen Keohane Marketing Manager: Michael Boezi Manufacturing Buyer: Evelyn Beaton Associate Production Supervisor: Julie LaChance Cover Design: Night and Day Design Cover Art: The Japanese Bridge ... set of problem-solving skills, and strengthening the students as learners of mathematics and science Anintegrated course offers freedom, new possibilities, and an invigorating freshness of outlook...
... Modifying the Graphs of Sine and Cosine 603 594 19.3 The Function f (x) = tan x 615 19.4 Angles and Arc Lengths 619 CHAPTER 20 Trigonometry—Circles and Triangles 627 20.1 Right-Triangle Trigonometry: ... VIII CHAPTER 22 Integration: An Introduction 711 Net Change in Amount and Area: Introducing the Definite Integral 711 22.1 Finding Net Change in Amount: Physical and Graphical Interplay 711 22.2 ... appreciate, and even come to share this excitement In some sense mathematics is a language—a way to communicate You can think of some of your mathematics work as a language lab Learning any language...
... vessel and blood pressure, an economist in the relationship between the quantity of an item purchased and its price, a grant manager in the relationship between funds allocated to a program and ... As another example, consider a hot-drink machine If your inputs are inserting a dollar bill and pressing the button labeled “hot chocolate,” the output will be a cup of hot cocoa and 55¢ in change ... representations may be confusing, but as you use the language of functions the nuances will become as natural as nuances in the English language Aside: In any discipline accurate communication is critical;...
... numbers and are included in the interval We indicate this on a number line by using filled circles at and 5 (2, 5) denotes the set of all numbers greater than and less than but excluding and themselves ... translate “A% of B” as A 100 · B If the tax is kx, where x is the price and k is a constant, we say that the tax is directly proportional to the price, with proportionality constant k We translate ... Earlier mathematicians, including such giants as Euler and Johann Bernoulli, thought of functions only as formulas, just as you perhaps did before starting this chapter (Howard Eves, An Introduction...
... so we’ll pause for a moment to clarify the meaning of an “if and only if” statement Language and Logic: An Interlude “A if and only if B” means “A and B are equivalent statements.” Using symbols ... way to relate h and r h success! relate r and 2-h using a triangle with hypotenuse Figure 1.12 We can relate r and h by looking at a cross-sectional slice and using a right triangle While it ... 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 cane will provide...
... For instance, suppose you were to calculate the value, V , of the change in your pocket V is a function of q, d, n, and p, where q, d, n, and p are the number of quarters, dimes, nickels, and pennies, ... starting out fresh and tiring at the end First Slice and Tass both run a mile in 1:12 On the same set of axes, graph F (t) and T (t), the distances traveled by First Slice and Tass, respectively, ... 1.16(a)–(c), 1.17(a) and (b), and 1.18(b) and (d) are, in fact, functions The test for a function is that every input must have only one output assigned to it; graphically, this means if we draw a...
... tile A, N, q, r, and m are constants (a) Give the number of tiles Amir and Omar can put down as a function of t, the number of hours they work together (b) How many square meters can they tile in ... done How many hours will it take Omar to finish the job alone? Express the answer in terms of any or all of the constants A, N, q, r, m, and H 59 Sam Wright plays the role of Sebastian the crab ... the patch? Express your answers in terms of any or all of the constants A, X, B, L, C, and T If you are having difficulty, use this time-tested technique: Give the quantity you are looking for...
... look at the graph of a function you can set the range and domain so that the scales are very different You should be aware that your choice of domain and range can make the line f (x) = x look almost ... + 3| > |2x − (−3)| > (the distance between 2x and −3) > We’ll focus on 2x and solve for x later 68 CHAPTER Characterizing Functions and Introducing Rates of Change –6 –5 –4 –3 –2 –1 Figure 2.16 ... Check that these answers satisfy the original equation ii Geometric Approach: |3 − x| = (the distance between and x) = 70 CHAPTER Characterizing Functions and Introducing Rates of Change x = or x...
... rate of change represents the slope of the line between the two points used This is because the average rate of change of f on [a, b] is given by change in output change in y rise = = , change in ... volume of water changes the height In the case of a cylindrical beaker we saw that the ratio change in height change in volume is constant We refer to this ratio as the rate of change of water ... notions: i Change in price is (final price − initial price) change in price ii Percent change in price is initial price (This gives percent as a decimal: 0.05 = 5%.) iii Average rate of change of...
... area changed? What is the average rate of change of area with respect to radius? ii When the radius increases from feet to feet, by how much has the area changed? What is the average rate of change ... 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 ... expansion (e.g., 1/4 = 0.25) or an infinitely ¯ repeating decimal (e.g., 1/6 = 0.16).13 An irrational number is a number that cannot be expressed as a ratio of integers The decimal expansion of an...
... than 25 square feet.) Rate of change : change in area = change in radius A A(3) − A(1) 8π = = = 4π r 3−1 ii Change in area: A(5) − A(3) = 25π − 9π = 16π Rate of change : change in area = change ... many holes in the graph of a function cause us such great consternation? Soon we will move from looking at an average rate of change of a quantity to inquiring about an instantaneous rate of change; ... Pythagoreans than it is causing for Ted Question: Between any two rational numbers, how many rational numbers are there? Answer: Infinitely many Question: Between any two rational numbers, how many...
... company gets by producing and selling x widgets, can be found by computing R(x) − C(x) Write the profit function and graph it (e) Find P (400) and P (700); interpret your answers Find P (401) and ... 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 g(x) = x ... widgets sold), so R(p) = p · D(p) Below is the graph of the demand function, where quantity demanded is a function of price.3 quantity demanded p1 Figure 3.5 (a) What prices will yield no revenue?...
... x –3 –4 –2 –3 –1 –2 –4 21 You put $300 in a bank account at 4% annual interest compounded annually and you plan to leave it there without making any additional deposits or withdrawals With each ... Find f (g(x)) and simplify your answer Be sure that your answer is in agreement with the concrete case from part (a) 3x and g(x) = 1−x (a) Find f (g(2)) and g(f (2)) (b) Find f (g(x)) and g(f (x)) ... x−3 and g(x) = x In Problems 39 through 43, find (f + g)(x), (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...
... −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 ... (x) (where k is a constant) relate to that of y = f (x)? You might want to break your answer into cases depending upon the sign of k and whether |k| is greater than, less than, or equal to i Does ... function at these peaks and valleys? (b) How does the graph of y = f (x) + k (where k is a constant) relate to that of y = f (x)? i Does adding a constant to f (x) change the location of its...