By Deborah Hughes-Hallett, Andrew M. Gleason, Daniel E. Flath, William G. McCallum, Eric Connally

Targeting a restricted variety of issues in additional intensity than could be widely used in a calculus textual content, this quantity emphasizes the which means, in useful, graphical, and numerical phrases, of the symbols used. Chapters conceal capabilities, the spinoff and the yes critical, short-cuts to differentiation, utilizing the spinoff, optimistic antiderivatives, integration, utilizing the sure imperative, approximations and sequence, differential equations, capabilities of a number of variables, vectors, differentiating services of many variables, optimization, integrating services of many variables, parameterized curves, vector fields, line integrals, flux integrals, and calculus of vector fields. comprises brief solutions to odd-numbered difficulties behind the ebook.

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45. Hydroelectric power is electric power generated by the force of moving water. 15 Strengthen Your Understanding In Problems 48–49, explain what is wrong with the statement. In Problems 50–52, give an example of: 48. 25x is decreasing and its graph is concave down. 50. 2 when t = 0. ” 49. The function y = 2x is increasing, and its graph is concave up. 51. 3x + 2. 52. A function with a horizontal asymptote at y = −5 and range y > −5. html. Accessed February 2011. html. Accessed February 2011. 16 Yearly values have been joined with segments to highlight trends in the data.

The function f was useful to athletes planning to compete with Bekele. Let us now change our point of view and ask for distances rather than times. 98 seconds of his race, the answer is clearly 4000 meters. Going backward in this way from numbers of seconds to numbers of meters gives f −1 , the inverse function18 of f . 98) = 4000. Thus, f −1 (t) is the number of meters that Bekele ran during the first t seconds of his race. 15, which contains values of f −1 . The independent variable for f is the dependent variable for f −1 , and vice versa.

When a piece of wood or bone was part of a living organism, it accumulated small amounts of radioactive carbon-14. Once the organism dies, it no longer picks up carbon-14. Using the half-life of carbon-14 (about 5730 years), we can estimate the age of the object. We use the following definitions: The half-life of an exponentially decaying quantity is the time required for the quantity to be reduced by a factor of one half. The doubling time of an exponentially increasing quantity is the time required for the quantity to double.

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