Recent content by Gagle The Terrible

Thanks a Ton Quasar ! And yes, I'm the guy sitting in front of you :P In the mean time, I had considered that approach. The details ought to come. EDIT : I got the first question right but thanks for your help. It assured me of my reasoning.

If I use the definition (i.e. there existe f : R^m\R^k --> S^(m-k-1) and g: S^(m-k-1) --> R^m\R^k such as f o g is homotopic to the identity ( of S^(m-k-1) ) and g o f is homotopic to the identity (of R^m\R^k) . To proove such homotopies , is the function h:[0,1]*X --> X given by...

I was asked to proove that R^m\R^k (m>k) has the same type of homotopy that S^(m-k-1) . I know I can use two criterias : the definition and the rectract criterium. The latter is more appealing because of it's "simplicity" but the function r:[0,1]*X --> X given by (1-t)x + tx/norm(x)...

I would really like to post the work I did, but it is gibberish ! I don't know how to tackle this integral : definite integral from 0 to 1 of : ln(x)ln(1-x)dx The "traditionnal" methods don't work but I assure you that I have tried much more ! Please help

S = 2 \pi \int_2^6 \sqrt{9x-18} \sqrt{1+ \frac{81}{36x-72}}dx S = 6 \pi \int_2^6 \sqrt{x-1/4} }dx Using the substitution u = x+1/4 you will get your answer Hope it helps.

I'd be carefull thought with manipulation regarding deifferentials. I remember in a differential geometry class the teacher had "split" ds^2 in ds*ds . But is true that in most cases, terms like dt^2 are said to be negligible comparatively to dt. Also, terms like dA sometimes refer to...

The thing I would like to know is if you are supposed to know the equation of the 30 *45 wall. It seems like a parabola but is it ? If you don't have the equation of the roof's curve, I really don't see how you can proceed analyticaly.

Even better !

I would divide it at the point (1,1) perpendicularly to the x-axis. Then the two regions are bounded by a constant and a straight line .

You can also try to complete the square or find the numbers m, n such as m*n = c and m+n = b when a = 1 .

If you are trying to integrate wrt x, try trig substitutions. If you are trying to integrate wrt y, try the substitution i mentionned earlier .

This is where the wisdom of hootnanny comes in play. Once you find du , you must find an expression with du where dy/5y can be "eliminated". You know that du = 2ydy. Therefore du/(10y^2) = dy/5y . From that, substitue y^2 again ... EDIT : Yo uare integrating with respect to what...

Perseverance, my friend, is the key to math. enlightment. In the worst case scenario, erase and start over. Try to figure it out by yourself, and if you really can't get to the answer, show what went wrong and then maybe...

try to substitute u = x^2 + y^2 Substitutions are a handy trick when the denominator is the derivative of the numerator.

How to do what ?