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x, y): =k is the set of all points in the domain of f at whi In other words, it shows where the graph of f has height Figure 11 the relation between level curves and horizontal

x, y): =k is the set of all points in the domain of f at whi In other words, it shows where the graph of f has height Figure 11 the relation between level curves and horizontal

Applications and Investigations in Earth Science (9th Edition)
Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Chapter1: The Study Of Minerals
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ition The level curves of a function f of two variables are the curves equations f(x, y) k, where k is a constant (in the range of f). = vel curve f(x, y) = k is the set of all points in the domain of f at which f takes en value k. In other words, it shows where the graph of f has height k. can see from Figure 11 the relation between level curves and horizontal traces. The arves f(x, y) = k are just the traces of the graph of f in the horizontal plane rojected down to the xy-plane. So if you draw the level curves of a function and e them being lifted up to the surface at the indicated height, then you can men- ece together a picture of the graph. The surface is steep where the level curves are ogether. It is somewhat flatter where they are farther apart. = 25 -k=201 FIGURE 12 -4000 -5500- 500 5000 LONESOME MTN Lonesome Creek e common example of level curves occurs in topographic maps of mountainous s, such as the map in Figure 12. The level curves are curves of constant elevation sea level. If you walk along one of these contour lines, you neither ascend nor nother common example is the temperature function introduced in the open- In the level curves are called isothermals and join loca-
Transcribed Image Text:ition The level curves of a function f of two variables are the curves equations f(x, y) k, where k is a constant (in the range of f). = vel curve f(x, y) = k is the set of all points in the domain of f at which f takes en value k. In other words, it shows where the graph of f has height k. can see from Figure 11 the relation between level curves and horizontal traces. The arves f(x, y) = k are just the traces of the graph of f in the horizontal plane rojected down to the xy-plane. So if you draw the level curves of a function and e them being lifted up to the surface at the indicated height, then you can men- ece together a picture of the graph. The surface is steep where the level curves are ogether. It is somewhat flatter where they are farther apart. = 25 -k=201 FIGURE 12 -4000 -5500- 500 5000 LONESOME MTN Lonesome Creek e common example of level curves occurs in topographic maps of mountainous s, such as the map in Figure 12. The level curves are curves of constant elevation sea level. If you walk along one of these contour lines, you neither ascend nor nother common example is the temperature function introduced in the open- In the level curves are called isothermals and join loca-
15 I 120 160 200 240 Day of the year X 36. Two contour maps are shown. One is for a function of whose graph is a cone. The other is for a function g whose graph is a paraboloid. Which is which, and why? II 8 B(m, h) 37. Locate the points A and B on the map of Lonesome Mountain (Figure 12). How would you describe the terrain near A? Near B? 12 280 38. Make a rough sketch of a contour map for the function whose graph is shown. = y m h² 39. The body mass index (BMI) of a person is defined by where in the person's mass (in kilograms) and h is the in R(m. h) = 18.5, other people with that s 80 kg. F 41-44 A contour map of a rough sketch of the graph c 41. 43. 4 14, 12 11 45-52 Draw a contc curves. 45. f(x, y) = x² - 47. f(x, y) = √x- 49. f(x, y) = ye* 51. f(x, y) = x² 53-54 Sketch bot compare them. 53. f(x, y) = x² 55. A thin metal T(x, y) at the mals) if the
Transcribed Image Text:15 I 120 160 200 240 Day of the year X 36. Two contour maps are shown. One is for a function of whose graph is a cone. The other is for a function g whose graph is a paraboloid. Which is which, and why? II 8 B(m, h) 37. Locate the points A and B on the map of Lonesome Mountain (Figure 12). How would you describe the terrain near A? Near B? 12 280 38. Make a rough sketch of a contour map for the function whose graph is shown. = y m h² 39. The body mass index (BMI) of a person is defined by where in the person's mass (in kilograms) and h is the in R(m. h) = 18.5, other people with that s 80 kg. F 41-44 A contour map of a rough sketch of the graph c 41. 43. 4 14, 12 11 45-52 Draw a contc curves. 45. f(x, y) = x² - 47. f(x, y) = √x- 49. f(x, y) = ye* 51. f(x, y) = x² 53-54 Sketch bot compare them. 53. f(x, y) = x² 55. A thin metal T(x, y) at the mals) if the
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