First, lets take a look at part a). When you have a composite function f(g(x)), whatever the x value is (or r value in this case), you plug that number in for g(x), whatever value that yields, you then plug into f(x). So for part a, the x values are all increasing from (2,4) on the r interval...
Integration by parts
I believe that if you try an integration by parts, with u=ln(x+1) and dv=1+x^2, that should get you stated--i believe will will have to do one more integration by parts and then some long division but i think that will get you to the end
I am working on a problem regarding arclength-which asks to find the arclength for r=2-2sinx (x=theta) I worked out the integral to the integral of the square root of 8-8sinx but i didnt know how to integrate from there--any help?
The sine of 45 degrees is equal to root two over two or approximately.7071. I was playing around on my calculator when i stumbled upon the resemblance that sine45 degrees is either equal to or extremely close to the sum from one to fifty of the (square root of x)/10. Is there anything here or...
The number 4 times out of five is a single prime #. It seemed a lot nicer when i posted it and in the first ten i checked 9 of them were single prime numbers. I have since found 3 more where the # is a multiple of 2 primes (2 and 3 in all cases). Thanks for at least looking at it Hurkyl
I am curious as to whether this pattern will always hold true:
Let's say we take the prime numbers:
and we take the square(individually) minus 1
3,8,24,48,120,168,288,360,528....p^2 - 1
Then starting with the third p^2 - 1 (24), all of the p^2 - 1 can...
If I am traveling at a good fraction of the speed of light (.9c for example) toward an object, how would the distance between the object and myself from my viewpoint compare to the that of an observers viewpoint
ya but aren't there different sized infinites, with cardinality and things of that nature? I mean i will concede that it is a stupid question, but for some reason i just imagine that there could be things like cantor dust, or fractional dimensions, but I guess not.
This may sound stupid, but it has always confused me. If you take a line and break it into infinitely smaller pieces, you would have miniscule lines while approaching infinity, yet at an "actual" infinity what is left is just points. What bothers me is, what happens inbetween. Is there some...
I was having this discussion in my math class today, and my teacher said that it was not something that he couldn't explain in a manner that we would understand. So the question is, are there more positive integers than primes, or no?
If you take away a set with measure of zero which is not empty, from something, like a line segment, do you alter the characteristics of that line. For example, taking away a point from a line makes it unconnected. Would the length change? I also don't understand how the measure would be zero...
I don't understand how you could be left with anything if you did it infinately many times. There shouldn't be anything left. What I understand, and I may be interpreting you wrong, but you would be left with a sort of "dust" similar to the cantor set. But the dust would be something. If you...
I get it, but there is something that is kind of bothering me. If instead of the middle thirds set, lets say we iterate a line segment of length one by removing a length of .9 every time. Why don't you get the same "dust"? And if you did, wouldn't that disprove that .99999...=1
the only problem with this is that logically there is an oldest son in both cases. For example, twins can both be born on the same day but one is always older. Did I miss something or am I just being too overanalytical?
Lets take the cantor middle thirds set as an example (Iterate by removing the middle portion of a line segment) If this was done an ACTUAL INFINITE number of times, would you be left with line segments, points, or neither?
I understand hhow to use the chain rule for a simple 2 part composite function, however, I tend to have problems when it gets past that. Can someone please help me master these complex derivatives, or just a few quick tips would be nice
I know that Einstein said that gravity is the curvature of spacetime, but I'm a bit confused as to what happens as a massive body moves through space. When a body is in a certain position, it warps that area of space, but as it moves past that particular area, how does the area of space that...
I have a chem test 2mor and i keep getting stuck on this problem
A 150.0g sample of metal at 75.0 degrees C is added to 150.0g of water at 15.0 degrees C. The temperature of water rises to 18.3 degrees C. Calculate the specific heat of the metal, assuming that all the heat lost by the metal...