134.sagews

# Some graphs for 15.1, #7

var('x,y')
f = sqrt(52 - x^2 - y^2)         # define the function
plot3d(f,(x,2,4), (y,2,6))       # plot f on the rectangular domain [2,4]x[2,6]

# Here I remove the default frame and add axes. I've also drawn the
# subrectangles we're asked to consider in the problem.
# The red dot is the "bottom left" corner of the domain.

functionplot = plot3d(f, (x,2,4), (y,2,6),frame=False)
axes = line3d([(0,0,0),(4,0,0)],arrow_head=True) + text3d("x",(4,0,-0.5)) +\
    line3d([(0,0,0),(0,6,0)],arrow_head=True) + text3d("y",(0,6,-0.5)) +\
    line3d([(0,0,0),(0,0,8)],arrow_head=True) + text3d("z",(-0.5,-0.5,8))
subrects = line3d([(2,2,0),(2,6,0),(4,6,0),(4,2,0),(2,2,0)]) +\
    line3d([(3,2,0),(3,6,0)]) +\
    line3d([(2,4,0),(4,4,0)])
bottomleftpoint = point3d((2,2,0),color="red")
functionplot + axes + subrects + bottomleftpoint