Transcript
MAT2454 - C´alculo II - POLI Alguns gr´aficos interessantes e suas curvas de n´ıvel 1. f (x, y) = 4x2 + y 2 4
y2
–1
–2
1 x
2
–2
gr´afico:
curvas de n´ıvel:
–4
2. f (x, y) = x2 − y 2 6 4 y 2 –4
–6
–2
0
2
x
4
6
6
7
–2 –4
curvas de n´ıvel:
gr´afico: 3. f (x, y) =
–6
y ,x > 1 x−1 4
y2
0
2
4 x
3
5
–2
gr´afico:
4. f (x, y) =
curvas de n´ıvel:
–4
x2 y x2 + y 2 6 y4 2 –6
–4
–2
0 –2 –4
gr´afico:
curvas de n´ıvel:
1
–6
2
x4
6
x2 − y 2 5. f (x, y) = 2 x + y2 4
y2
–4
–2
4
2 x –2
curvas de n´ıvel:
gr´afico:
6. f (x, y) =
–4
2xy 2 x2 + y 4 4
y2
–10 –8 –6 –4
–2
2
4 x6
8
10
–2
gr´afico:
7. f (x, y) =
curvas de n´ıvel:
–4
xy(x2 − y 2 ) x2 + y 2 4
y2
–4
–2
2 x –2
gr´afico:
curvas de n´ıvel:
2
–4
4
