Description
NINTH HOMEWORK
1. (10 pts) (5.2.13)
2. (10 pts) (5.2.14)
3. (10 pts) (5.3.4)
4. (10 pts) (5.3.13)
5. (10 pts) (5.4.13)
6. (10 pts) (5.4.14)
7. (10 pts) (5.4.21)
8. (10 pts) (5.5.3)
9. (10 pts) (5.5.4)
10. (10 pts) (5.5.9)
11. (10 pts) (5.5.11)
12. (10 pts) (5.5.12)
Just for fun: Find a bounded region D ⊂ R2 of type 3, so that
D = { (x, y) ∈ R2 | a ≤ x ≤ b, γ(x) ≤ y ≤ δ(x) } = { (x, y) ∈ R2 | c ≤ y ≤ d, α(y) ≤ x ≤ β(y) }
and a function f : D −→ R such that
� b
�� δ(x) �
f(x, y) dy dx, a γ(x)
exists but
� � d
�� β(y)
f(x, y) dx dy, c α(y)
does not.
Is the function f integrable over D?
1
18.022 Calculus of Several Variables
