Homework Statement
Not really a problem, more of a general question. When exactly can you use the Divergence test. Does it only work on both series and sequences?Homework Equations
The series Diverges if lim ƩAn ≠ 0
The Attempt at a Solution
If you take the lim of the series n^3/2n^3 ≠ 0 there...
So your saying that it takes longer than 2pi to complete before it starts tracing over itself again? and idea how i can find the time it takes a polar curve to complete 1 cycle?
Homework Statement
Find the area inside the larger loop and outside the smaller loop of the limacon r=.5+cosθ
Picture here http://www.wolframalpha.com/input/?i=r%3D.5%2Bcostheta
Homework Equations
Area = .5∫r^2The Attempt at a Solution
To get the area of the outer loop, you just get the value...
Homework Statement
Find the area enclosed by the graph r=2+sin(4θ)
Homework Equations
Area = .5∫r^2
The Attempt at a Solution
Area = .5∫(2+sin(4θ))^2
=.5(4.5θ-1/16sin(8θ)-cos(4θ))
I can do the integration and all, but I am having trouble finding the limits of integration
I...
Homework Statement
Find the area of the region that lies inside the curve r^2=8cos(2θ) and outside r=2Homework Equations
area of polar curves = .5∫R^2(outside)-r^2(inside) dθThe Attempt at a Solution
r^2=8cos(2θ) and r=2, so...
4=8cos(2θ)
.5=cos(2θ) since .5 is positive, we need the angles in...
If somebody could just do the entire thing via U substitution, that would be great. Then I can see how you did it. I'll be refreshing this page every few minutes.