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1. Find the probability it will be red

If the urn is selected at random, can't you just treated as if all the balls were in 1 huge urn? I think it's just 12/18 right?
2. God I hate recursive proofs so much

I've done 3 of my 5 problems, which took me 2 days and over 30-50 pieces of scrap paper. I'm serious, I didn't even eat dinner today because I spent straight hours just staring at questions, thinking I was coming close to solutions, then only to find out I've gotten no where. So in the end, I...
3. God, I hate Number Theory Proofs

I really really hate proofs! I've done 3 of my 5 problems, which took me 2 days and over 30-50 pieces of scrap paper. I'm serious, I didn't even eat dinner today because I spent straight hours just staring at questions, thinking I was coming close to solutions, then only to find out I've...
4. How do you deal with absolute values in your Integrals?

I have to solve the integral: \int^1_{-1} e^{-| |x| - \frac{1}{4} |} dx but I have no idea what to do with the absolute value signs. Can someone help me? :confused:
5. Integration by parts when a limit is infinity.

Ah, Thank you. I just noticed, when the x is an exponent, it increases the term much faster than when x is a base. So I can see how x^y / e^x will = 0 for all y. Thank you to all once again.
6. Integration by parts when a limit is infinity.

Ahh...I see what you're saying. Thank you. I don't mean to question your method, I know I might be becoming a nuisance by now, but can you tell me why \lim_{x \rightarrow \infty} x^ye^{-x} = 0 \ \forall y \in \mathbb{R}? I mean, doesn't \lim_{x \rightarrow \infty} x^y = \infty?
7. Integration by parts when a limit is infinity.

Hmm...maybe I should have mentioned this earlier, but I am not trying to solve the integral. I have to get it in a specific form so I can use Gaussian Quadrature. In order to do that I have to integrate by parts. The answer is supposed to be: \frac{1}{z + 1} \int_0^\infty x^{z + 1}...
8. Integration by parts when a limit is infinity.

But the way to calculate the gamma function is to do that actual integral... anywayz, do you see my problem though? when my v becomes v = \frac{1}{z + 1} x^{z + 1}, my x^{z + 1} term gets moved to the top and turns into infinity.
9. Integration by parts when a limit is infinity.

I'm having a tough time trying to do integration by parts with one of my limits being infinity. My Integral looks like: \int_0^\infty x^z e^{-x} dx with z = \frac{-1}{\pi} Now if I let u = e^{-x} and dv = x^z dx, I will have: du = -e^{-x} dx and v = \frac{1}{z + 1} x^{z + 1} and...
10. Finding limits of integration during a change of variables

Hi. I have a problem with a question. Basically, I have an integral that goes from x=0 to x=1, and I'm supposed to make a change of variables like this: Let x = 1 - y^2. The problem I'm having is trying to find the limits of integration after the change of variables. Since y = +/-...
11. Reducing 2nd order to 1st order type question

hmm...I didn't plug in anything, but my lecture notes says plug in back to original equation so I think you're on to something. If you're talking about the step where I went from y = (xp)/3, I moved the 3 to the LHS so it will be 3y = xp then I differentiated both sides 3y' = xp' + p...
12. Reducing 2nd order to 1st order type question

Help! I'm just starting this class and I have no idea what's going on. What I don't understand is, what answer are you supposed to give? My question says "Find the general solution and also the singular solution, if it exists". What the hell does that mean? Can someone tell me if this...