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)
Consider the region bounded by cos(x2) and the x−axis for 0 ≤ x
≤ ?(π/2)^1/2 . If this region is revolved about the y-axis, find
the volume of the solid of revolution. (Note that ONLY the shell
method works here).
f(x,y)=sin(2x)sin(y)
intervals for x and y:
-π/2 ≤ x ≤ π/2 and -π ≤ y ≤ π
find extrema and saddle points
In the solution, I mainly interested how to
findcritical points in case of the system of trigonometric
equations (fx=0 and fy=0).
,
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.
Find the roots of the following equation in [−π, π] 2x 2 − 4
cos(5x) − 4x sin x + 1 = 0 by using the Newton’s method with
accuracy 10^(−5) .
how do I solve this using a computer