The
following write-ups are due Monday May 8.
Monday May 1
Solve, write up and turn in:
Sec. 20.6: 3, 9, 13
Tuesday May 2
1. Find the volume of the
region in Example 2 Sec. 20.7 and find z.
Solve, write up and turn in:
Sec. 20.7: 1, 2, 3, 5
Wednesday May 3
Solve, write up and turn in:
Sec. 20.7: 11, 12, 19, 21
Thursday May 4
Sec. 20.8 Read the text of Examples 1 and 2, solve then check
your solutions.
Solve, write up and turn in:
Sec. 20.8: Set up double
integrals to calculate the areas: 1, 3, 5
Friday May 5
Denote by r the position vector r=(x,y,z)=xi+yj+zk.
Area of a surface given parametrically by r=r(t,s) with
(t,s) in D is
the double integral on D of dS=| rt
x rs | dt ds.
Solve, write up and turn in:
1. Consider the surface given parametrically by
x=t cos( theta), y=t sin(theta), z=theta
for 0 <t
< a , 0<theta<2Pi
a. Calculate the area of this surface.
b. Sketch the surface.
2. Consider the cone z=sqrt(x^2+y^2) for x^2+y^2<4.
Set up the integral (2) page 745 to calculate the area of this surface.
Is it correct to use this formula? Explain.
How can we avoid the difficulty?