15.1Ex44-45

15.1Ex44-45 - 620 C H A P T E R 15 D I F F E R E N T I AT I...

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620 CHAPTER 15 DIFFERENTIATION IN SEVERAL VARIABLES (ET CHAPTER 14) i B D E C P A ii iii 400 450 0 1 2 km Contour interval = 10 meters 470 iv 44. Match the contour maps (A) and (B) in Figure 23 with the two functions f ( x , y ) = x 2 y and g ( x , y ) = 2 x y . c = 2 y xx c = 2 c = 0 c = 2 c = 0 c = 2 2 2 1 2 1 y 2 2 2 (A) (B) 1 1 2 FIGURE 23 SOLUTION The level curves of the function f ( x , y ) = x 2 y are the lines x 2 y = c or y = x 2 c 2 .Theleve l curves of g ( x , y ) = 2 x y are the lines 2 x y = c or y = 2 x c . The slope of the lines in the contour map of g is greater than the slope in the contour map of f . Therefore (A) is a contour map of f and (B) is a contour map of g . 45. Which linear function has the contour map shown in Figure 24 (with level curve c = 0 as indicated), assuming that the contour interval is m = 6? What if m = 3? c = 0 6 3 6 3 1 2 2 1 x y FIGURE 24 We denote the linear function by f ( x , y ) = α x + β y + γ (1) The level curves of f are x + y + = c (2) By the given information, the level curve for c =
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This note was uploaded on 02/13/2010 for the course MATH MATH 32A taught by Professor Park during the Fall '09 term at UCLA.

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15.1Ex44-45 - 620 C H A P T E R 15 D I F F E R E N T I AT I...

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