Uni Maths Questions

[vcestudent94]

Can someone please check if I did this proof right? I've never done a 'formal' proof before so just need some reassurance to tackle the rest of the questions as they're all pretty similar. Cheers.



Edit: Sorry about the big picture, it wouldn't let me attach it.

[BigAl]

Can someone check the validity of this proof and answer my questions below?

[BigAl]

there is a typo up there
delta=sqrt(x^2+(y-1)^2, not -(y-1)^2

[humph]

Here's how I would write up my proof:

For and using shifted polar coordinates with , , so that , we can write

and so by the fact that and for all , together with the triangle inequality, we have that

for .
So for any , we let

and it follows by the previous argument that

implies that

for all . We therefore conclude that

[BigAl]

Here's how I would write up my proof:

For and using shifted polar coordinates with , , so that , we can write

and so by the fact that and for all , together with the triangle inequality, we have that

for .
So for any , we let

and it follows by the previous argument that

implies that

for all . We therefore conclude that

Thanks for formal maths...I finally end up with the same result as yours after realising that 2r^2 is much more proper function than 2r^3 for the values between 0 and 1. Thanks again

[Jeggz]

I would really appreciate help with this question guys! Thanks in advance

Consider the Inner product <f,g> =

Let and define D(a,b) = .
Minimise the function D and sketch both f(x) and the solution ax+b over [0,1]

[stolenclay]

Are you sure that's the right question? Because it doesn't seem to have a solution that you could get by hand...

Are you sure you don't mean ?

Spoiler

If you do mean that, then:


To minimise that, you could try partial derivatives. (Interestingly, it's also if you try and complete the square, but it's probably easier to use partial derivatives.)
Anyway, you should get that the minimum of is , with and .

Hopefully I didn't solve the wrong question.

[Jeggz]

OMG YES I DID MEAN THAT!
Thank you so much legend

[BigAl]

Just a general question. How do we find potential field such that F=Gradf ...isn't it just integratating component by component then adding them up?

[rife168]

Just a general question. How do we find potential field such that F=Gradf ...isn't it just integratating component by component then adding them up?

Yeah that's pretty much it, once you have determined that it is conservative and well defined and all that business...
Then when you integrate it's the case that you have 'constant' functions instead of the usual '+C' as in the case of single variables.

See here:
http://mathinsight.org/conservative_vector_field_find_potential