Description
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