Rates of Change and Behavior of Graphs

... change with constant rate of change, 712–714 difference between left- and right-hand sums and, 718–722 explanation of, 712 with nonconstant rate of change, 715–718 overview of, 711–712 Newton, ... integrals explanation of, 903 infinite interval of integration and, 903–907 method of comparison and, 912–914 methods to approach, 908–912 unbounded and discontinuous integra...

Ngày tải lên: 05/07/2014, 18:20

... Joan) Calculus: an integrated approach to functions and their rates of change / by Robin Gottlieb. Preliminary ed p cm ISBN 0-2 01- 70929-5 (alk paper) Calculus I Title QA303 G685 20 01 00-0 618 55 ... function and its derivative without being formally introduced to the derivative Part II focuses on rates of change and modeling using linear and quadratic f...

Ngày tải lên: 05/07/2014, 18:20

... Functions 421 Inverse Functions: Can What Is Done Be Undone? 421 12. 1 What Does It Mean for f and g to Be Inverse Functions? 12. 2 Finding the Inverse of a Function 429 12. 3 Interpreting the Meaning of ... and Arc Lengths 619 CHAPTER 20 Trigonometry—Circles and Triangles 627 20 .1 Right-Triangle Trigonometry: The Definitions 20 .2 20.3 20 .4 20 .5 Triangles We Know and...

Ngày tải lên: 05/07/2014, 18:20

... important and versatile We can attach many different mental pictures and representations to it; our choice of representation will often depend upon context Upon first exposure, the notation and ... 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 by x N EXAMPLE 1.2...

Ngày tải lên: 05/07/2014, 18:20

... price of a car and let f and g be the tax functions in states and 2, respectively We can describe the input-output relationship of the functions f and g using formulas f (x) = 500 g(x) = 0.04x The ... undefined; Equality of Functions The functions f and g are equal if: f and g have the same domain, and f (x) = g(x) for every x in the domain −x For example, the func...

Ngày tải lên: 05/07/2014, 18:20

... a panda needs to take in C calories for every pound of the panda’s weight i The number of pounds of sugar cane it takes to support a panda for a day is a function of the weight, x, of the panda ... discussions, 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 a...

Ngày tải lên: 05/07/2014, 18:20

... rectangular box has a square base Let s denote the 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 ... Consider the functions f , g, h, and k presented as graphs in Problems through 11 Which, if any, of these functions are 1 -to- 1? 38 CHAPTER Functions Are Lurking Everywher...

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... answers to parts (a) and (b) in terms of any or all of the constants A, X, B, L, and C (a) Express the number of bushels of huckleberries the two bears eat as a function of t, the number of hours ... the manufacturer decides to switch to plastic lids and bottoms to eliminate the taping problems Assume that custom-made plastic lids and bottoms cost 7k cents per squa...

Ngày tải lên: 05/07/2014, 18:20

... 0) and decreasing on (0, ∞) (d) j is undefined and discontinuous at x = (e) j is 1 -to- 1 Answers to Exercise 2.8 (a) g and h are even functions (b) f and j are odd functions (c) The graph of an ... Geometric Approach: |2x + 3| > |2x − (−3)| > (the distance between 2x and −3) > We’ll focus on 2x and solve for x later 68 CHAPTER Characterizing Functions and Introduci...

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... 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 from 1970 to 2000 (c) The average rate of change of the price of a cup of ... and (c).) (e) Illustrate your answers to parts (a), (b), and (c) by sketching f (x) and drawing secant lines whose slopes correspond to these average rates of ch...

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... 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 ... error is to be drawn in by the shape of a graph and leap headlong into a tangled web of incorrect conclusions without stopping to look at the labeling of the axes of...

Ngày tải lên: 05/07/2014, 18:20

... details and a very readable account, consult The History of Mathematics: An Introduction, by David Burton, McGraw-Hill Companies, Inc 1997 17 Due in part to their methods of record keeping and their ... climate, the ancient Egyptians and Babylonians have left modern historians more evidence of their mathematical development than have the people of other ancient civil...

Ngày tải lên: 05/07/2014, 18:20

... 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 ... We can say that S is equal to the composition of f and g Composition of functions is analogous to setting up functions as workers (or machines) on an...

Ngày tải lên: 05/07/2014, 18:20

... h(x) = f (g(x)) and j (x) = g(f (x)) What are the domains of h and j ? 35 f (x) = x + and g(x) = 36 f (x) = x+2 √ x and g(x) = x − 118 CHAPTER Functions Working Together 37 f (x) = x and g(x) = −2x ... 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) =...

Ngày tải lên: 05/07/2014, 18:20

... the output of f (a) How does the graph of y = kf (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 ... Learning to ask and answer questions that help you retain information is a large part of being a mathematician or scientist More Transformations of Output In addition to s...

Ngày tải lên: 05/07/2014, 18:20