A4-format til udskrift. - Aarhus Universitet

1. KONTINUITET 9
Grafen af f(x,y) = x 2 − y 2
1.8. Udseende saddel ☞ [S] 11.1 Functions of several variables
Figur
y
Niveaukurver for f(x,y) = x 2 − y 2
y = ± √ x 2 − 4
1.9. Halvkugleskal ☞ [S] 11.1 Functions of several variables
Eksempel 3,4,8
g(x,y) = 9 − x 2 − y 2
Grafen er en halvkugleskal
Niveaukurver er cirkler
Γg = {(x,y,z)|x 2 + y 2 ≤ 9,z = 9 − x 2 − y 2 }
= {(x,y,z)|x 2 + y 2 + z 2 = 9,z ≥ 0}
g −1 (k) = {(x,y)|x 2 + y 2 ≤ 9, 9 − x 2 − y 2 = k}
= {(x,y)|x 2 + y 2 = 9 − k 2 }
1.10. Globus ☞ [S] 11.1 Functions of several variables
Figur
z
x
Grafen for g(x,y) = 9 − x 2 − y 2
1.11. Breddegrader ☞ [S] 11.1 Functions of several variables
Figur
x
y