By James Stewart
Luck on your calculus direction starts off the following! James Stewart's CALCULUS texts are world-wide best-sellers for a cause: they're transparent, actual, and packed with suitable, real-world examples. With CALCULUS, 6th version, Stewart conveys not just the software of calculus that can assist you advance technical competence, but additionally grants an appreciation for the intrinsic great thing about the topic. His sufferer examples and integrated studying aids may also help you construct your mathematical self belief and attain your objectives within the direction!
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Additional resources for Calculus (6th Edition)
So f ͑x͒ increases three times as fast as x. Thus the slope of the graph y 3x Ϫ 2, namely 3, can be interpreted as the rate of change of y with respect to x. 5 FIGURE 2 V EXAMPLE 1 (a) As dry air moves upward, it expands and cools. If the ground temperature is 20ЊC and the temperature at a height of 1 km is 10ЊC, express the temperature T (in °C) as a function of the height h (in kilometers), assuming that a linear model is appropriate. (b) Draw the graph of the function in part (a). What does the slope represent?
In fact, it can be shown that by taking n large enough (that is, by adding sufficiently many terms of the series), we can make the partial sum sn as close as we please to the number 1. It therefore seems reasonable to say that the sum of the infinite series is 1 and to write 1 1 1 1 ϩ ϩ ϩ иии ϩ n ϩ иии 1 2 4 8 2 A PREVIEW OF CALCULUS |||| 9 In other words, the reason the sum of the series is 1 is that lim sn 1 nlϱ In Chapter 12 we will discuss these ideas further. We will then use Newton’s idea of combining infinite series with differential and integral calculus.
Y 20 x g x x x x x x _5 x 58. A taxi company charges two dollars for the first mile (or part of a mile) and 20 cents for each succeeding tenth of a mile (or part). Express the cost C (in dollars) of a ride as a function of the distance x traveled (in miles) for 0 Ͻ x Ͻ 2, and sketch the graph of this function. 59. In a certain country, income tax is assessed as follows. There is no tax on income up to $10,000. Any income over $10,000 is taxed at a rate of 10%, up to an income of $20,000. Any income over $20,000 is taxed at 15%.