By James Stewart, Daniel Clegg

New from James Stewart and Daniel Clegg, short utilized CALCULUS takes an intuitive, much less formal method of calculus with out sacrificing the mathematical integrity. that includes quite a lot of functions designed to inspire scholars with quite a few pursuits, transparent examples detailing vital mathematical methods, and an unlimited choice of workouts acceptable for college kids with disparate ability units, this primary variation is ideal for college kids who have to tips on how to practice calculus techniques instead of reflect the formal proofs in the back of the recommendations. Early insurance of exponential and logarithmic services enables the inclusion of many fascinating purposes through the textual content. on hand with more than a few vitamins together with improved WebAssign, short utilized CALCULUS makes calculus approachable so any scholar can comprehend the recommendations and succeed within the path.

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**Extra info for Brief Applied Calculus**

**Example text**

Therefore the scatter plot does not represent a function. (b) No matter where we draw a vertical line on the graph in Figure 15, the line will intersect the graph at most once, so this is the graph of a function. Notice that the “gap” in the graph does not pose any trouble; it is acceptable for a vertical line not to intersect the graph at all. ■ Mathematical Modeling Real-world problem In Example B on page 5, we drew a scatter plot of the world population data and then found an explicit equation that approximated the behavior of the population data.

We observe that if x ഛ Ϫ1, then f ͑x͒ 1 Ϫ x, so the part of the graph of f that lies to the left of x Ϫ1 must coincide with the line y 1 Ϫ x, which has slope Ϫ1 and y-intercept 1. ) If x Ͼ Ϫ1, then f ͑x͒ x 2, so the part of the graph of f that lies to the right of the line x Ϫ1 must coincide with the graph of y x 2, which is a parabola. This enables us to sketch the graph in Figure l7. The solid dot indicates that the point ͑Ϫ1, 2͒ is included on the graph; the open dot indicates that the point ͑Ϫ1, 1͒ is excluded from the graph.

15–20 ■ Find the functions p͑x͒ f ͑t͑x͒͒ and q͑x͒ t͑ f ͑x͒͒. 15. f ͑x͒ x 2 Ϫ 1, t͑x͒ 2x ϩ 1 16. f ͑x͒ 1 Ϫ x , t͑x͒ 1͞x 3 17. f ͑x͒ x ϩ 2x, 3 18. f ͑x͒ 1 Ϫ 3x, 19. f ͑x͒ x ϩ 1 , x 20. f ͑x͒ s2x ϩ 3 , t͑x͒ 1 Ϫ sx t͑x͒ 5x 2 ϩ 3x ϩ 2 t͑x͒ x ϩ 2 t͑x͒ x 2 ϩ 1 21. Surfboard production Let N͑t͒ be the number of surfboards a manufacturer produces during year t. If P͑x͒ is the profit, in thousands of dollars, the manufacturer earns by selling x surfboards, what does the function f ͑t͒ P͑N͑t͒͒ represent?