Please help me with whatever you're able to. And try to explain what's going on in the solving process. I want to understand this, not just get answers. Thank you so so much!!!

identify the curve by finding a cartesian equation for the curve:

r cos (theda) = 1

Find a polar equation for the curve represented by the given Cartesian equation:

x + y = 9

Find the area of the region that is bounded by the given curve and lies in the specified sector

r = e^(theta/2), pi less than or equal to theta less than or equal to 2pi

find the area enclosed by the curve

r = 2-sin(theta)

Find the area of the region that lies inside both curves

r = 1 + cos(theta), r = 1-cos(theta)

Determine whether the sequence converges or diverges. If it converges, find the limit.

a(n)= [(-1)^n * n^3]/[n^3 + 2n^2 +1]

{arctan 2n]

[ln(n)]/[ln(2n)]

Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?

a(n)=ne^-n