How to deduce is it \{\cos(\sqrt{2}t)(2+\cos t), \sin(\sqrt{2}t)(2+\cos t),\sin t \mid t \in \mathbb{R}\} submanifold of \mathbb{R}^3?
First, this is curve, so I was thinking to find point in which this curve has two intersect, and then some neighborhood of that point isn't homeomorphic to...
Nonononononono!
First of all l(v)=\displaystyle\int\limits_a^b f(x)vdx+c, NOT l(v)=\displaystyle\int\limits_a^b g(x)vdx+d. Who give you rights to say g(x) or d? NOBODY!
l(\alpha u + \beta v) = \displaystyle\int\limits_a^b f(x)(\alpha u + \beta v)dx + c, not +\alpha c + \beta c
Maybe you can prove it like standard proof of Cauchy–Schwarz inequality:
0 \le <x+\lambda y, x+\lambda y> = <x,x> + 2\lambda <x,y> + \lambda^2 <y,y>, and then choosing that \lambda = -\dfrac{<x,y>}{<y,y>} you will get |<x,y>|^2 \le <x,x> <y,y>
So, maybe, but maybe, you can use \lambda =...
Hi robertjford80!
I deleted my post because there was error in him (oh, bad English)
But, look at picture.
They said \int_0^6 \int_0^y x \mbox{d}x\mbox{d}y, that is yellow region (x from 0 (parallel y-axes) to x=y, y from 0 to 6). r is moving from r=0 to y=6, so, y= 6= r \sin \theta...
Hi :)
Can you recommend me some books about mathematics, but more philosophical focus
maybe
(i didn't read this book, so I don't know)
Sorry for bad English
Darboux sum is important here.
We define upper Darboux sum and lower Darboux sum, and say that function is Riemann-integrable iff \displaystyle\sup_{P}L_{f,P} = \displaystyle\inf_{P}U_{f,P} iff \forall \varepsilon>0 ~\forall P ~ \exists \delta>0~ \mbox{if} ~\lambda(P)<\delta ~\mbox{then}...
It looks like that for k=0 they use l'hopital's rule, because when k=0 you have 0/0 (but maybe this is not the limit). I don't know what is k,N,j, etc.
Because of my bad English, I will show how to do this problem:
Find the surface area of the portion of the cylinder x^2+z^2=b^2 lying inside the sphere x^2+y^2+z^2=a^2 where 0<b<a.
Solution: P=2P(S_1)=2\iint_{S_1}^{}\mbox{d}S=2\iint_{D}^{} \sqrt{1+(y_x)^2+(y_z)^2}\mbox{d}x\mbox{d}z where...