UoM Maths Thread

[kinslayer]

hello.
just wondering how i would use the sandwich theorem to figure out the limit of n!/n^n
thanks.

for n > 0,



and:



Can you finish from here?

[Inside Out]

oh wait yes i get it.. thanks heaps

[Inside Out]

okay so i get part a.
and then for part b i got the stationary points (0, 20^1/3), (0,0), (20^1/3,20^1/3) and (20^1/3,0). So i was just wondering how would you classify (0, 20^1/3), (0,0) and (20^1/3,0).
cheers.

[kinslayer]

okay so i get part a.
and then for part b i got the stationary points (0, 20^1/3), (0,0), (20^1/3,20^1/3) and (20^1/3,0). So i was just wondering how would you classify (0, 20^1/3), (0,0) and (20^1/3,0).
cheers.

S(x,y) is undefined for x = 0 or y = 0 so you're left with .

[Inside Out]

S(x,y) is undefined for x = 0 or y = 0 so you're left with .

does that mean all the other 3 points are neither a local maximum, local minimum or saddle point?

[kinslayer]

does that mean all the other 3 points are neither a local maximum, local minimum or saddle point?

The other three points aren't on the curve, so you don't need to classify them. The question is only asking for a point on the curve, nothing else. If you set and  , you will only get one point (x,y) that satisfies both equalities and also makes physical sense.

[Inside Out]

if fx (derivative of f)=4/(4x-5) what is fxy?

[notveryasian]

if fx (derivative of f)=4/(4x-5) what is fxy?

Is fx the partial derivative of the function f with respect to x? If so, then fxy=0, as all that is treated as a constant when differentiating with respect to y.

[Captain Rascal]

Hello err'body, I am have a royal rumble with the attached mathematical problem and I just can't muster the power to get the right answer. Specifically with the constant in the inhomogeneous boundary condition, which likely relates to an incorrect general solution. But anywho, if one kind soul would be willing to show me a step by step solution to this, I would be most thankful.
A similar problem is sheet 6 Q5 from the problem book (eng maths), which i also got wrong.

Best of luck with exams eeeeeeeeeeeveryone, i believe in you

[Phy124]

Hello err'body, I am have a royal rumble with the attached mathematical problem and I just can't muster the power to get the right answer. Specifically with the constant in the inhomogeneous boundary condition, which likely relates to an incorrect general solution. But anywho, if one kind soul would be willing to show me a step by step solution to this, I would be most thankful.
A similar problem is sheet 6 Q5 from the problem book (eng maths), which i also got wrong.

Best of luck with exams eeeeeeeeeeeveryone, i believe in you

Would you mind posting up your attempt so I can just point out where you went wrong, instead of writing up an entire solution

[hobbitle]

What Phy said ^
Those PDE questions can take almost half an hour :-P

[hobbitle]

PS where did that problem come from? It looks like from a past exam but most past exams don't make you solve for all three cases of the separation constant. Unless all three result in non-trivial solutions in this instance...

[Hancock]

The constant term will arise from the lambda = 0 case.
The cos term in the BC condition will arise from one of the other cases (lambda > 0 or < 0, ceebs figuring it out).

If you have two non-trivial solutions for varying lambda, you apply the principle of superposition. Let's say for instance that the other non-trivial solution for phi comes from the lambda < 0 case. Therefore you can say that:

phi (total) = phi (for lambda = 0) + phi (for lambda < 0)

Just make sure you properly find both functions for each case before superimposing them or it will screw up.

[Captain Rascal]

oh shoot, i figured out where i went wrong. Thanks for the help everybody. I expected it was from the lambda = 0 case but my math had failed me once again. Turns out with the 2 first order boundary conditions for x you get no info on the second integration constant, which i had just set to 0 absentmindedly.

But yea, thanks again and Hobbitle, it's Q10 from the sem 2 2012 paper on the LMS -- it was quite a long exam if i may say so myself, but at least they gave you an odd function for the Fourier series Q. I can just imagine on Wednesday getting into the exam and having to do all 3 cases + a complete Fourier series/integral question oh! the horror

[Inside Out]

use partial fractions to integrate: (x+13)/(x^3+2x^2-5x-6)
i can't work out how to factories the bottom polynomial.