# Search results

1. ### Marginal profits

So that definition would give the 'average rate of change of P(x)' i.e. change in profit/change in quantity For average profit which is the same as any average (arithmetic mean) i.e. total/quantity

3. ### Marginal profits

Where did you get your definition of average profit? Average profit = Total Profit/Quantity
4. ### Probability Spaces

OK well I am working with Probability and random processes By Geoffrey Grimmett, David Stirzaker, the google books preview covers the section i am dealing with (1.1 and 1.2 right at the start). This uses the definitions given in the exercise...
5. ### Probability Spaces

For 3 we need the union of any two intervals to be in G For the sigma field property we want all possible unions of all possible intervals to be in G Point 3 basically requires [0,x) be in G for x<=1, which we do have. In order for that sigma to hold we would need the interval (0,1) to be in...
6. ### Probability Spaces

Thanks yes! OK so we say A=[ai,bi)U[a(i+1),b(i+1)U...U[ar,br) Ac = omega/A Then 3 is now easy A=[ai,bi)U[a(i+1),b(i+1)U...U[ar,br) B=[aj,bj)U[a(j+1),b(j+1)U...U[as,bs) so AUB = [ai,bi)U[a(i+1),b(i+1)U...U[ar,br)U[aj,bj)U[a(j+1),b(j+1)U...U[as,bs) AUB=[ak,bk)U[a(k+1),b(k+1)U...U[at,bt)...
7. ### Probability Spaces

Homework Statement Let \Omega = [0,1) Let G be the collection of all subsets of \Omega of the form [a1,b1),\cup[a2,b2),\cup...\cup[ar,br) For r any non-negative integer and 0<=a1 and a1 <=b1 <= a2 .... Show that G is a field Show that G is not a \sigma-field Homework...
8. ### Determine whether the following series converges

I meant n>=5 :)
9. ### Determine whether the following series converges

So to conclude By the standard comparison test: since (1-1/n)^3 >= 1/2 for n>=2 and n\sqrt{1+n^{-7}+2n^{-8} <= 2n we must have \frac{(1-1/n)^{3}}{n\sqrt{1+n^{-7}+2n^{-8}}}\geq\frac{1/2}{2n}=\frac{1}{4n}\] More simply by the limit comparison test...
10. ### Determine whether the following series converges

Ah no i made a mistake! (again!!!) Limit comparison works, tends to 1 when i divide by 1/n. Thanks!
11. ### Determine whether the following series converges

No i meant for the comparison test, however if i use 1/n in the limit comparison i get an/bn tending to 0
12. ### Determine whether the following series converges

I do know the limit comparison however i just get the sequence tending to 0 rather than a finite L. So doesn't seem to be of use Comparison test should work for 1/4n, for n>=2 \frac{(1-1/n)^{3}}{n\sqrt{1+n^{-7}+2n^{-8}}}\geq\frac{1}{4n}\] So by comparison test the series diverges?
13. ### Determine whether the following series converges

I'm not thinking clearly at the moment, need a break, but I think 1/4n would work though for n>=3.
14. ### Determine whether the following series converges

I think the arbitrary term in my series is less than 1/n except for very small values of n below zero, so 1/n isn't suitable. With some manipulation we can express the nth term as as: \frac{(1-1/n)^3}{n\sqrt{1+n^{-7}+2n^{-8}}}
15. ### Determine whether the following series converges

Cheers, and crikey i made loads of mistakes in there - fixing :)
16. ### Determine whether the following series converges

Next question, if someone can tell me why my LaTex isn't working that would be fantastic ???
17. ### Determine whether the following series converges

Homework Statement Determine whether the following series converges: \sum \frac{(n-1)^3}{\sqrt{n^8+n+2}} Homework Equations Definition of convergence: Let \sum a_{n} be a series. If the sequence of (sn) partial sums converges to L (finite). Then we say the series converges to L or has...
18. ### Interesting logic problem

If he says yes in the first question you know he is lying so its on at 9. If he says yes in the second question you know he is telling the truth so its on at 10. If he says no in either case your at a dead-end, you would have to keep asking both questions till you got a yes. May be a better way...
19. ### Interesting logic problem

Is it true that you are lying and the football is on at 9? If he is telling the truth he will say no since he is not lying as the statement is always false when he is telling the truth. If he is lying then he will say yes if its on at 9 and no for 10. Using the and logical operator means he...
20. ### Integral of sinc(x)

Check out this proof of the dirichlet integral: http://en.wikipedia.org/wiki/Dirichlet_integral
21. ### Integral of sinc(x)

Think about euler's formula and leibniz. A 'simple' proof can be made this way.
22. ### Lower Level integration problem (Find the centroid)

We are using the constant multiple rule for integration and 1-sin^2=cos^2.
23. ### Lower Level integration problem (Find the centroid)

I'm guessing you have probably gone wrong somewhere unfortunately i don't know where. But the solution to your integral: http://www5a.wolframalpha.com/Calculate/MSP/MSP8641961aa713bih43db00000ebbd4gc0a51fd4i?MSPStoreType=image/gif&s=15 [Broken]
24. ### Partial derivative of an Integral

Thanks both, I think then if i let gu(x,v) = f(x, v) Then i will integrate as before to get \partial /\partial u [g(u,v)- g(a,v)]= g_{u}(u,v) so following on we can say if gu(x,v) = f(x, v) then gu(u,v) = f(u, v) (since x is the dummy variable) Would this be correct...
25. ### Partial derivative of an Integral

Homework Statement Show \partial /\partial u \int_{a}^{u} f(x,v) dx = f(u,v) Homework Equations The Attempt at a Solution Basically i understand that we hold all other variables constant, and i understand that we will get our answers as a function of u and v. But to show that we have...