Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 63 docx

... Modifications of the Functions, and Vice Versa? To change the balance line of a sine or cosine function is to shift the function vertically (and vice versa). To change the amplitude of a sine or cosine ... versa). We know how to shift a function vertically and how to stretch and shrink both hori- zontally and vertically, so we simply apply our knowledge to these ne...

Ngày tải lên: 05/07/2014, 18:20

... peaks and valleys? (c) 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 2 .Onthe same set of axes sketch the graphs of f(x )and ... decompose the function and find its rate of change from our knowledge of the rates of change of these simpler functions. 8 PROBLEMS FOR SECTION 3.3 1. Let h(x) =f(g(x...

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... definition of derivative to find f  (x). Use your work to check your answers to parts (a) and (b). 19. The domain of a function f is all real numbers. The zeros of f(x)are x =−1, x = 2, and x = ... and formulas for derivatives of √ x and 1 x found in Chapter 5 to arrive at a formula for the derivative of x n for n = 0, 1, 2, 3, −1, and 1 2 . Try your formula on anot...

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... growing a crop of tomatoes wants to know when he should harvest and sell them in order to collect the most revenue. Both the weight of the crop and the price of tomatoes are changing over time. ... for any exponent, but we will not be able to prove this until we know more about exponential functions, their inverse functions, and taking the derivative of composite func...

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... great deal, so you need to be loose and limber with exponential algebra. You need to know exponential functions like the back of your hand. You will want to be able to picture an exponential function ... In order to understand the progress of the disease it is necessary to understand the growth of a population of E. coli. 3 Recall that y is proportional to x means...

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... −π and 2π and a y-intercept of −2. (a) Draw a graph of f  . (b) Write an equation for f  . This equation should have no unknown constants. (c) On the graph you drew in part (a), go back and ... encountered in the case of functions f , g, and h above. Now consider the functions j(x)= 1 x for x = 0 and 0 for x = 0ork(x ) = (x 2 ) for x = 0 and 1 for x = 0, both res...

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... below illustrate. 11 CHAPTER APortrait of Polynomials and Rational Functions Linear functions, quadratics, and cubics are all members of the larger family of polynomial functions, a family whose members are functions that can be ... Exploratory Problems for Chapter 10 371 21. The graph below shows the total cost and total revenue curves for a certain firm. Both revenue and...

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... (g(x)) in terms of f , g, and their derivatives. Our assumption throughout is that f and g are differentiable functions. Many functions we can’t yet differentiate can be decomposed and expressed ... can be shown that both dg dt =0 and df dt =0, so the equation df dt = df dg · dg dt still holds. Let’s return to the fish and make things more concrete. Suppose we want to find...

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... introduction into the environment occurs at regular intervals. Geometric sums are important to investors in analyzing and comparing investment schemes and to banks in calculating payments on loans and mortgages. ... finely.) As I hand you pieces of pie you accumulate more and more of the pie. The more slices I hand you, the closer you will come to having the entire pie. You c...

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... asks Angie if he should buy it. Angie says that she thinks he needs to know about the interest rates and how many years he’ll have to make the monthly payments. Barry listens to the radio again and ... is made to you today and the 20th payment 19 years later. Let’s compute the “up-front value” of the prize money of 20 annual payments of $50,000. The first payment of $50...

Ngày tải lên: 05/07/2014, 18:20