Prove $\lim_{(x,y)\to (0,0)} \frac{x^2 y^3}{x^4 + y^4} =0$ without $\varepsilon - \delta$.
Multivariable Delta Epsilon Proof $\lim_{(x,y)\to(0,0)}\frac{x^3y^2}{x^4+y^4}$ --- looking for a hint
How to keep a constant baselineskip when using minipages (or \parboxes)? When a minipage is used to box a text paragraph, the first line of the minipaged text and the last line of the previous text paragraph are closer than two consecutive lines in a standard text paragraph; analogously, the last line of text inside the minipage and the first line of text after the minipage are also closer.  The following MWE illustrates this:  \documentclass{article} \usepackage{lipsum}  \newcommand\Text{Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis. Curabitur dictum gravida mauris. Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna.\textbullet}  \begin{document}  \Text  \noindent\begin{minipage}{\linewidth} \Text \end{minipage}  \Text  \end{document}   How can I guarantee a constant baseline-skip even if minipages (or \parboxes) are used? What should I do when my neural network doesn't learn? I'm training a neural network but the training loss doesn't decrease. How can I fix this?  I'm not asking about overfitting or regularization. I'm asking about how to solve the problem where my network's performance doesn't improve on the training set.    This question is intentionally general so that other questions about how to train a neural network can be closed as a duplicate of this one, with the attitude that "if you give a man a fish you feed him for a day, but if you teach a man to fish, you can feed him for the rest of his life." See this Meta thread for a discussion:   If your neural network does not generalize well, see: I want to make a bootable USB thumb drive to install Windows on my computer. I don't want to use my old DVD to create an image and then upgrade to SP1, so I decided to download an untouched .iso file that already has SP1 in it. My question is this, is there a difference between these two files files?     en_windows_7_home_premium_with_sp1_x64_dvd_620851.iso   vs     en_windows_7_home_premium_with_sp1_x64_dvd_u_676549.iso   What does dvd_u mean, is it somehow different from plain dvd? Also will these work with my retail Home Premium key or do these work only for thoe with TechNet/MSDN accounts? C99 stdint.h header and MS Visual Studio I already derived a QM expectation value for ordinary momentum which is: $$ \langle p \rangle=  \int\limits_{-\infty}^{\infty} \overline{\Psi}  \left(- i\hbar\frac{d}{dx}\right) \Psi \, d x $$ And I can read clearly that operator for momentum equals $\widehat{p}=- i\hbar\frac{d}{dx}$. Is there an easy way to derive an expectation value for $\langle p^2 \rangle$ and its QM operator $\widehat{p^2}$? Handling jQuery Component Collision In plugin development, what is the best practice to prevent jQuery component collision on the front end?  For instance, let's say I include the jQuery Apprise dialog in a plugin that loads this on the front-end for something, yet another plugin may do the same. Because this gets loaded and declared twice, or perhaps one is forked and customized while mine is not, we get Javascript errors on the frontend (I assume).  (Note that I'm doing the best practice of using the wp_register_script() and wp_enqueue_script() strategy via a wp_head() action event in order to load a jQuery component on the frontend.) Limit- almost finished, however hint needed. Sum of nth roots of unity Question: If $c\neq 1$ is an $n^{th}$ root of unity then, $1+c+...+c^{n-1} = 0$  Attempt: So I have established that I need to show that $$\sum^{n-1}_{k=0} e^{\frac{i2k\pi}{n}}=\frac{1-e^{\frac{ik2\pi}{n}}}{1-e^{\frac{i2\pi}{n}}} =0$$ by use of the sum of geometric series'. My issue is proceeding further to show that this is indeed true. Why does main method in Java always need arguments? Shape of a string/chain/cable/rope/wire? The height of a string in a gravitational field in 2-dimensions is bounded by $h(x_0)=h(x_l)=0$ (nails in the wall)  and also $\int_0^l ds= l$. ($h(0)=h(l)=0$, if you take $h$ as a function of arc length) .  What shape does it take?  My try so far: minimise potential energy of the whole string,  $$J(x,h, \dot{h})=\int_0^l gh(x) \rho \frac{ds}{l}=\frac{g \rho }{l}\int_0^l h(x) \sqrt{1+\dot{h}^2} dx$$  With the constraint  $$\int_0^l \sqrt{1+\dot{h}^2} dx- l=0$$ If it helps, it's evident that $\dot{h}(\frac{l}{2})=0$.  Generally, this kind of equation is a case of a constrained variational problem, meaning that the integrand in  $$\int_0^l \frac{g \rho }{l}h(x) \sqrt{1+\dot{h}^2} +\lambda(\int_0^l \sqrt{1+\dot{h}^2} dx- l)dx$$  Must satisfy the Euler Lagrange equation. The constraint must also be satisfied.  But, in truth, by this point I am clueless. $\lambda$ is worked through $\nabla J  = \lambda \nabla(\int_0^l \sqrt{1+\dot{h}^2} dx- l)$. I have tried this , but get nonsensical answers.  Is this method the best? If so, in what ways am I going about it wrongly thusfar? Method for determining irreducibles and factorising in $\mathbb Z[\sqrt{d}]$ I know that $\mathbb Z[\sqrt{7}]$ is a UFD, and I can write the equation $(2 + \sqrt{7})(3 - 2\sqrt{7}) = (5 - 2\sqrt{7})(18 + 7\sqrt{7}) $. So clearly these are not all irreducibles. How do I determine which of these aren't irreducible? How do I factor those into irreducibles?  It seems difficult when dealing with $\mathbb Z [\sqrt{d}] $ with $d$ positive, since the norm map isn't as nice (it's not always positive).  Thanks I can prove the converse of it, but I cannot do this one. Here is the problem:     Prove that the implicit function theorem implies the inverse function theorem. I have the following element element(by.css(&quot;span[aria-label='Picker ID, TESTUSER']&quot;)  I want to assure the text on this filed is TESTUSER, so I tried:  expect(element(by.css(&quot;span[aria-label='Picker ID, TESTUSER']&quot;)).getAttribute('value')).toEqual('TESTUSER');  then I got the error: Expected null to equal 'TESTUSER' So I tried: element(by.css(&quot;span[aria-label='Picker ID, TESTUSER']&quot;)).getText().then(function (value) {         console.log(value);       })  And I got this error: Expected '' to be 'TESTUSER'.  How to get the value of this field and expect it is TESTUSER? I want to add a check constraint on a column if entered value for column is greater than 3 than it should be saved as 1 else entered value. For that scenario I am using below query but on insertion of data it shows an error message.  create table tblTestCheckConstraint  ( id int, NewColumn int )   alter table tblTestCheckConstraint add constraint chk_tblTestCheckConstraint_NewColumn1 CHECK   (     CASE         WHEN NewColumn &gt;4 THEN 1         ELSE NewColumn     END = 1 )   Insert Statement:   insert into tblTestCheckConstraint values ( 1,5) insert into tblTestCheckConstraint values ( 1,2)   Error Message:   Msg 547, Level 16, State 0, Line 1 The INSERT statement conflicted with the CHECK constraint "chk_tblTestCheckConstraint_NewColumn1". The conflict occurred in database "DBName" , table "dbo.tblTestCheckConstraint", column 'NewColumn'. The statement has been terminated. I need to somehow retrieve the client's IP address using JavaScript; no server side code, not even SSI.  However, I'm not against using a free 3rd party script/service. Grid System in LaTeX JavaScript variable definition: Commas vs. Semicolons First we are told that the Galactic Empire/Federation/Powers-that-be have kept the Earth locked up for being too warlike, but now their help is needed against invaders from another galaxy.  When the aliens land the first thing they meet is a talking bunny.      at the end when humans have accepted to join the fight the alien offers to send ships to transport them. The human leader tells that there is no need...  and the Earth accelerates away.   I must have read this sometime in the mid eighties, so no later than 84 or 85, but the story may be from the sixties or before. Should I do anything when I see several references that are not used in the text? In a linguistics paper I read, I noticed that several references in the bibliography are not actually used in the text. This is for about 10-15% of the references the case. Should I do anything with this? I always thought that all references must be used in the text, because even if they are just suggestions for further reading you would want some explanation why it is relevant and what you can find where.   I only know the author through their work and do not know the editors. The paper is from 2011. The references are rather general. They are relevant to the paper, but you would want page numbers with them unless you are familiar with them. They are all from different authors and different institutes. It is likely that the references were used in previous versions of the text. Repeating an equation including its content and number