... since ** evaluation ** ** of ** such ** parsers ** with goldstandard data is extremely problematic A major drawback ** of ** our methodology is that the ** evaluation ** is indirect ** and ** the results depend on a selected task ** and ** ... ** and ** Katrenko ** and ** Adriaans (2006), while Sætre et al (2007) presented better results than theirs in the same ** evaluation ** criterion Related Work Though the ** evaluation ** ** of ** ** syntactic ** ** parsers ** has been ... community, ** and ** a couple ** of ** works have recently presented the comparison ** of ** ** parsers ** based on different frameworks, ** their ** methods were based on the comparison ** of ** the parsing accuracy in terms ** of ** a certain...

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... 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 integrands ** and,** 907–908 use ** of,** 903 ... ** functions,** 334–338 historical background ** of,** 211 instantaneous rate ** of ** change ** and,** 209–211, 711, 983 ** of ** inverse trigonometric ** functions,** 703–706 limit deﬁnition ** of,** 190, 191 local linearity ** and,** ...

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... 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 ** functions ** Linearity ** and ** interpretation ** of ** ... course, at the instructor’s discretion ** Part ** I provides ** an ** introduction ** to ** ** functions ** ** and ** ** their ** representations with ** an ** emphasis on the relationship between meaning ** and ** symbolic ** and ** graphic representations...

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... ** 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 ** Love, ** and ** the Information They Give ... Limits ** and ** Continuity ** 24** 5 7.1 7 **.2 ** Investigating Limits—Methods ** of ** Inquiry ** and ** a Deﬁnition ** 24** 5 Left- ** and ** Right-Handed Limits; Sometimes the ** Approach ** Is Critical 7.3 7.4 N CHAPTER ** 22** 6 A Streetwise Approach...

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... 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 Functional notation ** and ** ... 1.2 What Are ** Functions?** Basic Vocabulary ** and ** Notation A is a function with domain {1, 2, ** 3,** 4, 5} ** and ** range {c, d, g, o, s}.4 B is a function with domain {1, 2, ** 3,** 4, 5, 6} ** and ** range {c, d} C...

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... 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 ** functions ** f (x) = x x ** and ** g(x) = x − ... at ** and ** 5 (2, 5) denotes the set ** of ** all numbers greater than ** and ** less than but excluding ** and ** themselves x ∈ (2, 5) is equivalent ** to ** < x < (2, 5) is called ** an ** open interval because neither ** of ** its...

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... 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 are equivalent statements.” Using ... constants S, N, ** and ** C ii The 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...

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... 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 Everywhere 13 The graphs ** of ** f ** and ** g are ... graph ** of ** a function? y y (a) y y (b) (c) (d) x x x x Figure 1.18 Answer We can tell that the relationships represented in Figures 1. **16(** a)–(c), 1.17(a) ** and ** (b), ** and ** 1.18(b) ** and ** (d) are, in fact, functions...

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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 square inch Express the cost ** of ** ... amount ** of ** gravel in the pile as a function ** of ** its (a) height (b) radius 1.3 Representations ** of ** ** Functions ** 45 50 In Durham, England, the circular plots ** of ** land at the center ** of ** the roundabouts **17 ** are...

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... 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 ** Introducing ** Rates ** ** of ** Change –6 –5 ... 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 ** functions...

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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 ** change Answer the previous question ... Simplify your answer 80 CHAPTER Characterizing ** Functions ** ** and ** Introducing ** Rates ** ** of ** Change (d) [1, + h] (Show that your answer agrees with the answers you obtained in parts (a), (b), ** and ** (c).) (e)...

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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 ** the graphs You can be misled ... Characterizing ** Functions ** ** and ** Introducing ** Rates ** ** of ** Change Exploratory Problems for Chapter Runners Early one morning three runners leave Washington State University in Pullman ** and ** run the Palouse Path11 joining...

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... 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 civilizations The writings ** of ** the Greek ... –20) 94 CHAPTER Characterizing ** 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...

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... 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 ** assembly line If the output ** of ** g is handed ... the output ** of ** j is the quotient ** of ** the outputs ** of ** f ** and ** g The product is g(x) deﬁned for any x in the domains ** of ** both f ** and ** g; the quotient is deﬁned for any x in the domains ** of ** both f ** and ** g provided...

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... 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) = 5x − 41 f (x) = 2x + ** and ** ... output ** of ** another function N EXERCISE 3.11 There are many ways ** of ** decomposing ** functions ** For instance, suppose h(x) = x2 + x2 + ** and ** we want ** to ** ﬁnd f ** and ** g such that f (g(x)) = h(x) Determine which of...

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