Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 5 pptx

... 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. ... 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 o...

Ngày tải lên: 05/07/2014, 18:20

... 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 ... average rate of change of the function g over the interval [6, 6 + h] C. The average rate of change of the function h over the interval [6, 6 + h] ii. One of the func...

Ngày tải lên: 05/07/2014, 18:20

... To find upper and lower bounds for P(2)means that we must find a price that is greater than P(2) and a price that is less than P(2).For instance 51 <P(2)< 75, so 51 is a lower bound and 75 ... equilibrium price and quantity? Assume price is measured in dollars and quantity in thousands of units. (The equilibrium occurs when supply and demand are equal.) (9, 12) 16 12 p...

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... 5. 1 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 ... f(x) h . 5. 1 Calculating the Slope of a Curve and Instantaneous Rate of Change 1 85 ix. Find the slope of the line through (2, 0) and (1.998, f(1.998)). x. Find the slope...

Ngày tải lên: 05/07/2014, 18:20

... ? 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 stronger than that ... 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...

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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 ... symmetry. Any random polynomial may be even, odd, or neither. The following example is meant to illustrate criteria for a function to be even and to be odd. ◆ EXA...

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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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... 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) 2 x 2 2 x = ... B, and log C are just constants, so the equation is analogous to 3 + 5f(x)=7g(x). 2. If you want to solve for a variable and it is caught inside a logarithm, (i.e., in the...

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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 59 9 cos x is an even function; ... ways. Historically it developed in the context of triangles, and hence the name of this family of functions refers to triangles. We will take a triangle...

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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 ... lbs/ft 3  · ( 45 − y i ) ft ·  area of the ith strip  50 20 45 0 5 Water level Depth = 45 – y i y i y 0 y 1 y n y x (20, 50 ) Top of dam Face of dam . . . ....

Ngày tải lên: 05/07/2014, 18:20