Calculus (7th Edition) by James Stewart

By James Stewart

Good fortune on your calculus path starts off the following! James Stewart's Calculus texts are around the world best-sellers for a cause: they're transparent, exact, and choked with suitable, real-world examples. With Calculus (Seventh Edition), Stewart conveys not just the application of calculus that can assist you improve technical competence, but additionally grants an appreciation for the intrinsic great thing about the topic. His sufferer examples and integrated studying aids can assist you construct your mathematical self assurance and attain your targets within the direction!

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Example text

Figure 1 was recorded by an instrument operated by the Cali- y fornia Department of Mines and Geology at the University Hospital of the University of Southern California in Los Angeles. Use it to estimate the range of the vertical ground acceleration function at USC during the Northridge earthquake. 1 0 2 1 x 4. The graphs of f and t are given. (a) State the values of f ͑Ϫ4͒ and t͑3͒. (b) For what values of x is f ͑x͒ ෇ t͑x͒? 6. In this section we discussed examples of ordinary, everyday functions: Population is a function of time, postage cost is a function of weight, water temperature is a function of time.

C. The cost C of mailing an envelope depends on its weight w. Although there is no simple formula that connects w and C, the post office has a rule for determining C when w is known. D. The vertical acceleration a of the ground as measured by a seismograph during an earthquake is a function of the elapsed time t. Figure 1 shows a graph generated by seismic activity during the Northridge earthquake that shook Los Angeles in 1994. For a given value of t, the graph provides a corresponding value of a.

B) Since t͑2͒ ෇ 2 2 ෇ 4 and t͑Ϫ1͒ ෇ ͑Ϫ1͒2 ෇ 1, we could plot the points ͑2, 4͒ and ͑Ϫ1, 1͒, together with a few other points on the graph, and join them to produce the graph (Figure 8). The equation of the graph is y ෇ x 2, which represents a parabola (see Appendix C). The domain of t is ‫ޒ‬. The range of t consists of all values of t͑x͒, that is, all numbers of the form x 2. But x 2 ജ 0 for all numbers x and any positive number y is a square. So the range of t is ͕ y y ജ 0͖ ෇ ͓0, ϱ͒. This can also be seen from Figure 8.

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