1) find the are of the region that lies inside of the curve r=
1+ cos theta and outside the curve r=3 cos theta.
2) find the sum"
En=1 3^{1-n}:2^{n+2}
3) find
integration ( 2x^2 +1) e^x^2 dx
4) Does:
E n=12 ((2n)!/(n!)^2) converge or diverge ? justify your answer
( what test?)
Use a double integral to find the area of the region. The region
inside the cardioid r = 1 + cos(θ) and outside the circle r = 3
cos(θ). Can someone explain to me where to get the limits of
integration for θ? I get how to get the pi/3 and -pi/3 but most
examples of this problem show further that you have to do more for
the limits of integration but I do not get where they come
from?
Problem 2.
(a) Find the electric potential inside (r<R) and outside
(r>R) a uniformly charged solid sphere (with the charge density
roe) whose radius is R and whose total charge is Q. Use infinity as
your reference point. Plot schematically V(r) as a function of
r.
(b) [15%] By using the result for the electric potential in the
previous part, calculate the electric field in each region (r>R
and r<R)