# Search results

1. ### Trinomial and Multinomial theorem

Okay, thanks but I still don't understand the multi variable summation notation- What does the i,j,k under the sigma represent and why is there nothing on "top" of the sigma? Does this notation also assume that: "the summation is meant to be over all triples i, j, k where...
2. ### Help in proof of a theoreom

Well, we just learned that the lim x -> a notation simply means that the x value is approaching a, but it isn't a. So it is the value right next to a. I guess it's just a practical and less formal way of saying the same thing, although simply saying that x minus a is greater than zero...
3. ### Help in proof of a theoreom

"Given ϵ>0 , there exists δ1>0 " Where did ϵ and δ come from? I don't recall learning this at all when learning limits.
4. ### Trinomial and Multinomial theorem

I can't understand the sum notation shown in Wikipedia or in this article: http://mathforum.org/library/drmath/view/53159.html I want to find the sum notation for (a+b+c)^n however I can't understand the sum notation: I don't understand the use of brackets or what they mean here and in the...
5. ### Surface area and volume of a sphere

Can you find the surface area of a sphere without using the cylinder formula? (I mean, you can end up with the same formula, but you use different reasoning)
6. ### Education and economic growth

Okay, is there a better way of stating my example? Is this okay: Diminishing returns especially happen when, for example, a man chooses to major in a state college (with state scholarships) only to choose to live off his wife upon completion of the degree. Of course he may have some...
7. ### Education and economic growth

Sorry, I didn't mean to make anyone mad. It could have easily been a man who lives of his wife, I just stated the traditional scenario. "If that same woman enhances the education (and moral compass) of her children - there is an absolute value to society that should not be diminished - IMO."...
8. ### Education and economic growth

On the what to teach, shouldn't practical things such as cooking, car mechanics, and personal accounting be required for a GED? Specially since these skills don't require high levels of abstract thinking and can be learned through apprenticeship, the skills can be more easy for younger...
9. ### Nonlinear integration using integration factors?

The above method is too tedious, here is a better way: dy/dx = Q - ay - by^3 dx/dy = \frac{1}{Q - ay - by^3} dx = \frac{dy}{Q - ay - by^3} Now integrate both sides (I don't know how to do it) but Wolf math does...
10. ### Nonlinear integration using integration factors?

I'm not sure this is right, but it may work!: dy/dx + (a+b.y^2)y = Q dy/dx + ay+by^3 = Q dy/dx = Q - ay - by^3 y = Qx - a\int(ydx-b\int(y^3dx Now we convert dx into dy and y terms: dy/dx = Q - ay - by^3 dx = \frac{dy}{Q - ay - by^3} Bam! Here it is y = Qx -...
11. ### What is high level mathematics really like?

Thanks for the reply, it's cleared up some things and I think I get it now. Euclid's proof shows that if P + 1 is not prime, then P + 1 can not be divided by a prime number in the finite set of prime numbers since when you divide P + 1 by a factor of P, that factor will end up dividing 1...
12. ### A question that give wrong answer?

Why can't we make a equal some function? a = -8x \frac{a}{-8}=\frac{-8x}{-8} Here the function is globally onto. I don't understand why you choose y=0 in the discriminant: Delta = 6^2-4(-8)a instead of Delta = (6 - 6y)^2 - 4(a + 8y)(-8 - ay) We can either replace a for one function...
13. ### What is high level mathematics really like?

I don't understand how this part is valid: "If q is not prime then some prime factor p divides q. This factor p is not on our list: if it were, then it would divide P (since P is the product of every number on the list); but as we know, p divides P + 1 = q. Then p would have to divide the...
14. ### A question that give wrong answer?

I think you can still use the quadratic equation: a has to be a value that makes this expression always true (since you can't take the square root of negative numbers): http://latex.codecogs.com/gif.latex?0\leq&space;(6-6y)^2-4(a&plus;8y)(8&plus;ay) I'm not sure what you do next...
15. ### A question that give wrong answer?

I thought this expression had to be negative for there not to be any zero roots in the denominator. a> -\frac{9}{8} Why isn't that ^ the answer? I don't understand what onto and f:R-->R mean. If you plug in any number less than -9/8 on any graphing calculator, you will get a continuous...
16. ### A question that give wrong answer?

Oh, I think I know what it is know. Isn't it weird how there is an -8 on top where there is an a in the bottom and vise versa? You simply put in a=-8 and the answer is always 1! ((-8)*x^2+6x-8) / ((-8)+6x-8*x^2)=1 -8 is smaller than -9/8 so the calculus was true. I don't quite get what...
17. ### A question that give wrong answer?

Okay, so I'm just going to treat the top equation as a quadratic, and the bottom equation as a quadratic, and then multiply them together. Now I replace the first fraction with a,b, and c with a,6, and -8. Then I replace the second fraction with a,b, and c with -8, 6, and a. Now you...
18. ### Function for orbits based on time.

Okay, I am trying to find a formula for the position of two bodies (or more) in space based on the initial velocity and time. I'm trying to integrate the equation for gravitational acceleration to find the velocity equation, however, the radius is changing, and the degree (theta) is also...
19. ### What is this equal to?

DArN iT! I thought I had found a way around it though. Have you at least tried it this way? I have another hunch: and look! \lim_ {N\rightarrow +\infty}{\frac{1}{N}\sum_{k=0}^N{(\frac{L}{N}k)^{(\frac{Lk}{N})}}} Which is so close to: \lim_ {N\rightarrow...
20. ### How to factor out the b from e^(ab)

But Hey! According to wikipedia: http://en.wikipedia.org/wiki/The_fundamental_theorem_of_calculus ,this image: ,and this formula: When you take the derivative of a remain sums, the last sum times dx should be your answer. In this case, I did not have a dx because I'm...
21. ### What is this equal to?

\lim_{N\rightarrow +\infty}{\frac{1}{N}\sum_{k=1}^L{1^k}}=1 L=Nh (it doesn't let me put two characters on top of the sigma) It's 1^k right? nvm it always equals 1. Oh, I think that what I meant was from k=1 or 0 to k=Nh not N on the sigma sign. So, is what I wrote above right? It...
22. ### What is this equal to?

It seems to go toward 1
23. ### What is this equal to?

\lim_{N\rightarrow\infty} \lim_{h\rightarrow 0} \frac{1}{N}\sum_{k=0}^N((kh)^h)^k= and Nh=L h = L/N
24. ### Weighing Options: Should I Take AP Stats?

Based on my friends, AP Stats was really easy, compared with Physics AP (but then again Since Physics AP deals with the application of Calculus to Physics and we were learning Calculus in the same year, we had some blind spots until the end of the year when we learned Calculus). One of my...
25. ### How to factor out the b from e^(ab)

I'm trying to find the average value of x^4 from 0 to L So, I simply made an infinite number of function values be divided by the number of those function values: (h)^(4) + (2h)^(4) +...(Nh)^(4) N P.S: Nh=L I factored out the h^4...: [(1)^(4) + (2)^(4) +...(N)^(4)](h)^(4) N...
26. ### How to factor out the b from e^(ab)

Yeah, you're right. So, how many other ways are there of doing integrals and derivative? You can ignore the following rant: "I didn't like the whole "work backwards" process for finding the integrals of function, so I tried to find the average value then multiply that value by the length...
27. ### How to factor out the b from e^(ab)

I must have done something wrong. There shouldn't be a -1 next to the 2^L. You wouldn't happen to know a a formula that would get (2^L)/(log(2)L) or how we can edit the original conditions to remove that -1 in the end. I have hunch that dividing the original sigma by N+1 instead of N might...
28. ### How to factor out the b from e^(ab)

That's Awsome! Thanks for showing that to me Mute. The following is true, right?: ^{lim}_{N\rightarrow\infty}\frac{1}{N}\sum_{k=0}^N{^{lim}_{h\rightarrow0}(2^h)^k}=\frac{1}{N} 2^h \frac{1-2^{hN}}{1-2^h}=\frac{h}{L}\frac{e^h}{1-e^h}(1-e^{L})=\frac{2^L}{log(2)L} (Nh=L) I have a feeling...
29. ### How to factor out the b from e^(ab)

Has anyone here heard of discrete calculus? I think that's what I'm trying to do, but the most advanced math course I've taken is Calculus I so I don't understand how you reduced the original Sigma equation to this: \frac{1}{N} e^h \frac{1-e^{hN}}{1-e^h} ? The guy at this website talks...
30. ### How to factor out the b from e^(ab)

I'm trying to find the average of an infinite series. We have an infinite number of subdivisions: N subdivisions All of the subdivision's lengths are equal and virtually zero: h length If we multiply the subdivisions (h) by the number of them (N) we should get the length of all of them...
31. ### How to factor out the b from e^(ab)

\frac{1}{N}\sum_{k=1}^N{(e^h)^k}=\frac{1}{N} e^h \frac{1-e^{hN}}{1-e^h}=\frac{e^L}{L} and Nh=L I know that it should equal (e^L)/L but I don't know why. Here's another situation: 2^(h)+2^(2h)...2^(Nh) N Nh=L (based off of what you had-I don't know if this is right though)...
32. ### How to factor out the b from e^(ab)

I'm not sure how you got the right part of that equation (induction?). Could you show me the logic behind it or at least tell me what math course that you take to learn that sort of stuff? Using whatever you have there, Can you prove that it equals: e^L L ?
33. ### How to factor out the b from e^(ab)

What was that? I think I had the mute button on. Here's what I meant e^(h) + e^(2h)... e^(Nh) N I want to factor out the h's, so that I have something like: [e^(1) + e^(2)... e^(N)][something] N
34. ### How to factor out the b from e^(ab)

Well... I have two limits: h-> 0 N-> infinity When I multiply these limits together, I get a constant: Nh = L I have the following "thing" (since it's not a function or is it?): e^(h) + e^(2h) +...e^(Nh) N If we can factor out the h from ^ that ^, then we can put it to the side...
35. ### How to factor out the b from e^(ab)

I want to know if there is a way to factor out the b from e^(ab) so that: e^(ab) = e^(a)[f(b)] or e^a + f(b) or e^(ab) = some other function where a and b are separated.
36. ### Limit of a sequence (I think)

Sorry, I got it.
37. ### Constrained Least Square Optimization

Sorry, but I'm curious- What is this? I don't recognize the aT thing or the double absolute value marks. Could you tell me what type of math is this? Is it Calculus III?
38. ### Confusion about the constant of integration and bounds

When we integrate a derivative: What are the bounds? Shouldn't we then have this if the bounds are x2 and x1: but instead we have this:
39. ### Gravitational Potential Energy can be negative?

I think I'm having a definition problem. If potential energy is the energy that you could potentially use. How can you use energy that you don't have, or energy that is negative? Does it have to do about where E mech is? So potential energy is the negative work done by a field (or spring)...
40. ### What is the integral of dy/f'(x)?

I am dealing with polynomials (and other functions) which are continuous and always differentiable. If g(y) = x and f(x) = y, then I thought that g'(y) = dx/dy, since f(x) = dy/dx so the integral of dx/dy + C= g(x) What I think you are saying is g(y) = the integral of (dx/dy)(dy/dx) + C then...
41. ### What is the integral of dy/f'(x)?

Can you integrate this function (perhaps by using integration by parts)? I know it depends on what f(x) is, but we can use general notation such as f''(x) or the integral of f(x) so that we can simply plug in for any f(x). The point of this equation is to solve for x when f(x) is a big...
42. ### Gravitational Potential Energy can be negative?

What you are saying is that the Mechanical Energy is zero at infinity? Then what would happen if the net mechanical energy positive or negative? If I am doing work against gravity, my potential energy is positive and it increases since my work has contributed to the increase in potential energy...
43. ### F=μmg. How was μ calculated? Obviously experiments were

If you ignore the air particles, then the normal force (or what you call n) should be zero (since there isn't any normal force, since we are ignoring internal forces). If you don't ignore the air particles, then the air particles hit against the falling body (which causes the momentum of the...
44. ### Gravitational Potential Energy can be negative?

I have two physics books that state that U(r) = -GMm/r What I don't understand,is how can potential energy be negative? I've done the integral of GMm/r^2 from infinity to r, but I don't quite get the concept of negative potential energy. I don't understand why using r=infinity as...
45. ### What is the integral of dy/f'(x)?

@ homology dy/dx = f'(x)dx Your right, it is false: dy/dx = f'(x)dx/dx = f'(x) Still, that doesn't change the question since I originally just ignored dx (because the change in f(x) per dx or that the f'(x) is based on dx)
46. ### What is the integral of dy/f'(x)?

Well... I found a cool trick to find the derivative of the inverse of functions What I originally took the derivative of y: dy/dx = f'(x)dx Then I flipped the derivative: dx/dy = 1/f'(x)dx If we solved for y and took the derivative of it with respect to y, you would get the...
47. ### Practical Meaning

I think he means an easy explanation for them. A limit is a value that a function approaches. For example, you are lifting weights one day and you decide to increase the weights at small increments. Eventually you will approach a maximum amount of weight or what you may call your limit. If...
48. ### What is the integral of dy/f'(x)?

Yes, I'm trying to integrate that function. Using this method: u = f'(x) and dv = dy I want to integrate this function enough times to see a pattern. While integrating, I keep in mind that f(x) is the function of a polynomial. When integrating it is preferable to derive any f''''''(x)...
49. ### What is the integral of dy/f'(x)?

If x = the integral of dy/f'(x) what is a x equal to? I used integration by parts. I'm trying to integrate it enough times to find a pattern (using f'''''' notation so I don't get lost). I'm having trouble doing it. If anyone can spot something please share!
50. ### The derivative of f(x)*g(x)/h(x)

Thank you, I was trying to verify if that worked by doing it both ways. I figured out my problem. I had the signs on the v(x)/h(x) derivative rule switched.