Skip to main content

Active Calculus - Multivariable

Activity 12.3.3.
In this activity, we will be breaking the region \(D\) from the previous example into parts which are horizontally or vertically simple.
(a)
In Figure 12.3.15, we have broken our region \(D\) into two regions \(V_1\) and \(V_2\text{.}\) Give inequalities for each of \(V_1\) and \(V_2\) that shows that they are individually vertically simple.
Figure 12.3.15. The region \(D\) split into two regions, \(V_1\) and \(V_2\text{,}\) which are individually vertically simple
(b)
In Figure 12.3.16, we have broken our region \(D\) into three regions \(H_1\text{,}\) \(H_2\text{,}\) and \(H_3\text{.}\) Give inequalities for each of \(H_1\text{,}\) \(H_2\text{,}\) and \(H_3\) that shows that they are individually horizontally simple.
Figure 12.3.16. The region \(D\) split into three regions, \(H_1\text{,}\) \(H_2\text{,}\) and \(H_3\text{,}\) which are individually horizontally simple