Choose the general slicing method, the disk/washer method, or
the shell method to find the volume of the following solids.
The region bounded by the curves y=x+1, y=12/x, and y=1 is
revolved about the x-axis. What is the volume of the solid that is
generated?
The region bounded by y=(1/2)x, y=0, x=2 is rotated around the
x-axis.
A) find the approximation of the volume given by the right
riemann sum with n=1 using the disk method. Sketch the cylinder
that gives approximation of the volume.
B) Fine dthe approximation of the volume by the midpoint riemann
sum with n=2 using disk method. sketch the two cylinders.
If the infinite curve y = e−3x, x ≥ 0, is rotated about the
x-axis, find the area of the resulting surface. (answer needs to be
in fraction form if possible)
Given:
f(x,y) = 5 - 3x - y for 0 < x,y < 1 and x + y < 1, 0
otherwise
1) find the covariance of x and y
2) find the marginal probability density function for x
c) find the probability that x >= 0.6 given that y <=
0.2