Line 1 x3 Line 2 6x1 Line 3 10x1 H42 l In the file MATH 251

l. In the file MATH 251 Project I Region pdf and next to your name, the equations of three lines are provided that form a region on the plane z 0. Write the lines that define your region and draw the region. 2. Prove that the triangular region of question I lies inside the circle that is defined as the intersection of the elliptic paraboloid z(r, y)- H-x -y2 and the plane z 0 3. Find the volume of the solid that lies below the paraboloid, above the plane z and within the region of question l. The value of parameter H is provided in the last column. 4. Graph the 3D surface z(x, y). 5. Reevaluate the volume by choosing a different order of integration. Show all your work to obtain maximum credit.

Solution

1)

clear; clc;
x = 0:0.1:10;
y1 = x-3;
y2 = -6*x+1;
y3=10*x-1
plot(x,y1,\'color\',\'r\'); hold on;
plot(x,y2,\'color\',\'b\');hold on;
plot(x,y3,\'color\',\'g\')