Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 19 pptx

... dollars and quantity in thousands of units. (The equilibrium occurs when supply and demand are equal.) (9, 12) 16 12 p q supply demand 4. A moving company charges a minimum of $250 for a move. An ... SLOPE OF A CURVE AND INSTANTANEOUS RATE OF CHANGE In Chapter 4 we looked at linear functions, functions characterized by a constant rate of change. This characteristic is uni...

Ngày tải lên: 05/07/2014, 18:20

... 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. ... Representations of Functions 29 199 0 199 1199 2199 3199 4199 5199 6199 7199 8199 9 13000 14000 15000 16000 17000 year 18000 Applicants to Harvard Collegetemperature time Fig...

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... the graph of a famil- iar function and applying appropriate shifts, flips, and stretches. Label all x- and y-intercepts and the coordinates of any vertices and corners. Use exact values, not numerical ... section of this chapter to the pocketful of functions you’ve been introduced to (the identity, squaring, reciprocal, and absolute value functions) , graph the follo...

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... Calculating the Slope of a Curve and Instantaneous Rate of Change 183 the slope of the secant line through P and Q. By choosing Q successively closer to P , guess the slope of the tangent line at P ... Let P and Q be points on the graph of f with x-coordinates 3 and 3 + h, respectively. (a) Sketch the graph of f and the secant lines through P and Q for h = 1 and h...

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... a double thickness of aluminum. (a) Give an expression for the volume of the can. (b) Give an expression for the amount of material used. (Remember that the top and bottom of the can are two layers ... ? 14. A can for mandarin oranges is a cylinder with volume of 250 cubic centimeters. Denote the radius by r and the height by h. The material used for the top and bottom is...

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... quadratic that we can factor. = x(x − 4)(x + 2) So, the zeros are x = 0, x = 4, and x =−2. ◆ 1 From Howard Eves, An Introduction to the History of Mathematics, and David Burton, A History of Mathematics. 11.2 ... or not the answer to the problem is unique. Explain and/ or illustrate your answer. 9. A fourth degree polynomial with zeros of multiplicity two at x = 2 and x =−3...

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... noticed this and proceeded to look for the inverse analytically, we would soon realize that there was a problem. Set y = x 2 and then interchange the roles of x and y to obtain an inverse relationship. x ... 1 -to- 1 on its natural domain it is possible to restrict the domain in order to make the function invertible. Note that the domain of f is the range of f −1 and t...

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... Ke x + K = Le x − L, where K and L are constants and 0 <K<L (d) R(1 + n) nx = (P n) x , where P , R, and n are constants (e) 3b x = c x 3 2x , where b and c are constants 5. Solve for x. (a) ... x. SOLUTION Think of what was done to x and undo it. Remember that because you put on your socks and then your shoes, your shoes must come off before your socks. To construct t...

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... coordinate axes u and v because we want x to determine the point P , making sine and cosine functions of x. 19. 1 The Sine and Cosine Functions: Definitions and Basic Properties 599 cos x is an even function; ... x (b) Figure 19. 4 In Example 19. 2 and Exercise 19. 3 we approximated the values of sin x and cos x for various values of x.Ifxis any integer multiple o...

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... methods of transforming a difficult integrand into something more manageable. In the final section of this chapter we expand our notion of integration to encompass unbounded integrands and/ or an unbounded ... scientific energy toward understanding it. We build bridges to travel over it, tunnels to travel under it, dams to contain it, plumbing, draining, and irrigation systems...

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