Calculus Early Transcendentals by James Stewart

By James Stewart

Luck on your calculus path begins right here! James Stewart's CALCULUS: EARLY TRANSCENDENTALS texts are world-wide best-sellers for a cause: they're transparent, actual, and jam-packed with correct, real-world examples. With CALCULUS: EARLY TRANSCENDENTALS, 8th version, Stewart conveys not just the software of calculus that will help you enhance technical competence, but in addition provides an appreciation for the intrinsic fantastic thing about the topic. His sufferer examples and integrated studying aids might help you construct your mathematical self belief and accomplish your ambitions within the direction.

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If f ͑x͒ ෇ x2 Ϫ x xϪ1 and (c) (d) (e) (f) Estimate the solution of the equation f ͑x͒ ෇ Ϫ1. On what interval is f decreasing? State the domain and range of f. State the domain and range of t. t͑x͒ ෇ x is it true that f ෇ t? y g f 3. The graph of a function f is given. (a) (b) (c) (d) (e) (f) whenever x 1 Ͻ x 2 in I State the value of f ͑1͒. Estimate the value of f ͑Ϫ1͒. For what values of x is f ͑x͒ ෇ 1? Estimate the value of x such that f ͑x͒ ෇ 0. State the domain and range of f. On what interval is f increasing?

Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 1 y D The graph shown in Figure 22 rises from A to B, falls from B to C , and rises again from C to D. The function f is said to be increasing on the interval ͓a, b͔, decreasing on ͓b, c͔, and increasing again on ͓c, d͔. Notice that if x 1 and x 2 are any two numbers between a and b with x 1 Ͻ x 2 , then f ͑x 1 ͒ Ͻ f ͑x 2 ͒. We use this as the defining property of an increasing function.

Velocity When we look at the speedometer of a car and read that the car is traveling at 48 mi͞h, what does that information indicate to us? We know that if the velocity remains constant, then after an hour we will have traveled 48 mi. But if the velocity of the car varies, what does it mean to say that the velocity at a given instant is 48 mi͞h? In order to analyze this question, let’s examine the motion of a car that travels along a straight road and assume that we can measure the distance traveled by the car (in feet) at l-second intervals as in the following chart: t ෇ Time elapsed (s) 0 1 2 3 4 5 d ෇ Distance (ft) 0 2 9 24 42 71 Copyright 2010 Cengage Learning.

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