That answer is more than enough. If I am understanding it correctly, the size of the gravitational redshift is too small to really worry about, but it would be hard to tell the difference between them if we really needed to?
From what I understand:
1. The more massive the object, the stronger the gravitational field. This leads to the light being emitted from the surface to shift down in frequency.
2. The rate of expansion of the universe causes a redshift proportional its distance away.
I'm new to this, but...
LCKurtz is right, how could I be so silly, you can still get to the ellipse in cartesian, but for the bounds you will definitely need polar coordinates of some sort.
Well, the curve given is a circle with radius 1.
This can be verified: The equation of a circle is
x2+y2=r2
since you were given:
x=cos(b)
y=sin(b)
x2+y2=r2 goes to:
cos2(b)+sin2(b)=r2
1=r2
1=r
If you draw the circle and the line y=x, which according to the problem is...
yeah, I added an attachment, to my previous post, that shows the two paraboloids from the top. If you find the function for the boundary shape, you can find your bounds of x and y. Remember, you only need xmin xmax ymin and ymax
I recommend two things:
1. No change of variables or coordinate systems, it just makes things more intricate.
2. Find the bounds first. They aren't as complex as you would imagine.
All of this assuming, you will use a double integral.
To find the upper paraboloid just evaluate the...
I am confused by eq. 1 and 2. You converted (1) from cartesian to "wonky" cartesian. You have the equation of the normal line as y=x, which is correct, but that second equation seems to come out of nowhere.
What does the original function actually represent? If you graph the curve, and y=x...