By James Stewart

Good fortune on your calculus direction starts off right here! James Stewart's CALCULUS texts are world-wide best-sellers for a cause: they're transparent, actual, and packed with correct, real-world examples. With CALCULUS, 6th version, Stewart conveys not just the software of calculus that can assist you improve technical competence, but in addition grants an appreciation for the intrinsic fantastic thing about the topic. His sufferer examples and integrated studying aids may help you construct your mathematical self belief and accomplish your pursuits within the direction!

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**Example text**

33– 44 Find the domain and sketch the graph of the function. 19. The number N (in millions) of cellular phone subscribers worldwide is shown in the table. ) t 1990 1992 1994 1996 1998 2000 N 11 26 60 160 340 650 (a) Use the data to sketch a rough graph of N as a function of t. (b) Use your graph to estimate the number of cell-phone subscribers at midyear in 1995 and 1999. 20. Temperature readings T (in °F) were recorded every two hours from midnight to 2:00 PM in Dallas on June 2, 2001. The time t was measured in hours from midnight.

When Achilles reaches the point a 2 t1, the tortoise is farther ahead at position t2. When Achilles reaches a 3 t2 , the tortoise is at t3 . This process continues indefinitely and so it appears that the tortoise will always be ahead! But this defies common sense. a¡ a™ a£ a¢ a∞ ... t¡ t™ t£ t¢ ... Achilles FIGURE 9 tortoise One way of explaining this paradox is with the idea of a sequence. The successive positions of Achilles ͑a 1, a 2 , a 3 , . ͒ or the successive positions of the tortoise ͑t1, t2 , t3 , .

This function arises in physics and chemistry in connection with Boyle’s Law, which says that, when the temperature is constant, the volume V of a gas is inversely proportional to the pressure P: 1 0 |||| x 1 V FIGURE 14 C P The reciprocal function where C is a constant. Thus the graph of V as a function of P (see Figure 15) has the same general shape as the right half of Figure 14. V FIGURE 15 Volume as a function of pressure at constant temperature 0 P Another instance in which a power function is used to model a physical phenomenon is discussed in Exercise 26.