Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 3 ppsx

... we want to indicate that the function Q assigns to the input of 3 the output of 16. We write Q (3) = 16 name of function input output We read this aloud as “Q of3 is16.” 5 5 You can think of the ... 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 5 1.2 WHAT ARE FUNCTIONS? BASIC...

Ngày tải lên: 05/07/2014, 18:20

... Guardino, Sara Anderson, Michael Boezi, Susan Laferriere, and Barbara Atkinson. And thanks to Elka Block and Frank Purcell, for their comments and suggestions. Finally, I want to thank the following ... Optimization 36 5 CHAPTER 11 A Portrait of Polynomials and Rational Functions 37 3 11.1 A Portrait of Cubics from a Calculus Perspective 37 3 11.2 Characterizing Polyn...

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... f(x)=x 2 and g(x) =−2x +3 38. f(x)= x x 3 and g(x) = 2 x In Problems 39 through 43, find (f + g)(x), (fg)(x), and  f g  (x), and find their domains. 39 . f(x)=ax + b and g(x) = cx + d 40. f(x)=3x + 2and ... , g, and h are defined for all integers. At the top of the following page is a table of some of the values of these functions. 3. 2 Composition of Functions...

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... points (π ,3 )and (−π,5) 8. Passing through point ( √ 3, √ 2) and parallel to 3x − 4y = 7 9. Passing through the origin and perpendicular to πx − √ 3y = 12 10. x-intercept of √ π and parallel to the ... passing through points P and Q, where P and Q are points of the graph of f(x)with the indicated x-coordinates. 14. f(x)= 3 x + 2x; the x-coordinates of P and Q...

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... words, you are asked to find the family of functions with a constant slope of 32 . (b) Pick out the one function in the family of functions found in part (a) that is relevant to our situation by ... unknown constants, a, b, and c. 5 If one of the points we know happens to be the vertex of the parabola (and we are aware of that), then the parabola is determined by jus...

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... shifting, and of graphing 1 f(x) ;check your graph with your graphing calculator. Your answers to parts (a) and (b) ought to agree with your answer to part (c). You can use your answers to parts (a) and ... 11.4 Rational Functions and Their Graphs 409 numerator and the denominator of the rational function. We will use the fact that for any positive integer n and...

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... The price and the demand for a certain item can be modeled by the equation 20p =−q+200. (a) Express the rate of change of quantity demanded with respect to price in terms of a derivative and evaluate ... price and quantity can both be thought of as functions of time. At a certain instant the price is $6 and is increasing at a rate of $0.25 per week. At what rate is the...

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... A, B, and C are positive constants and y =A sin(Bx +C). What are the period and amplitude of the sine graph? Describe the horizontal shift. 19 .3 The Function f(x)=tan x 617 The Zeros of tan x. ... numerator and denominator are positive. The numerator is increasing and the denominator is approaching zero, so tan x grows without bound. tan(−x) = sin(−x) cos(−x) = − sin x cos x =...

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... Giza to estimating the sizes and distances of the sun and the moon. A triangle has three sides and three angles. To solve a triangle means to find measures for all three sides and all three angles ... triangles often include the terms “angle of elevation” and “angle of depression.” Angle of elevation refers to the angle from the horizontal up to an object; angle...

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... equal subintervals, each of length x, and form left- and right-hand Riemann sums, L n and R n , respectively. Explain and illustrate the following. If f  > 0, then L n <  3 −1 f(x)dx <R n ;and if f  < ... quantity can be represented as the signed area under the graph of the rate of change function. The question of how to find the area under the graph of...

Ngày tải lên: 05/07/2014, 18:20