As for the domain, the only restriction comes from the logarithm. The argument of a logarith must be strictly positive, so we have
As for the range, we have:
- The range of
are all real numbers - If we change to
we're translating the function horizontally, so the range remains the same - If we change to
we're stretching the function horizontally, so the range doesn't change - If we change to
we're translating the function 1 unit up, but the range is already all the real numbers, so it doesn't change.
You need to find out how many pints are in 2,4,6,8 quarts. by the way 1 quart equals 2 pints. so to start you off. 2 quarts would be 4 pints and so on
Parameterize the lateral face
of the cylinder by
where
and
, and parameterize the disks
as
where
and
.
The integral along the surface of the cylinder (with outward/positive orientation) is then
