For 2017 the IRA contribution limit is $5500 and 401k contribution limit is $18,000. Could you contribute $5500 to the IRA and $18,000 to the 401k in the same year or are you limited to one account or the other?
Can I deduct a contribution to a traditional IRA if I am also contributing to a 401(k) in the same tax year?
Suppose that $f$ is differentiable on $\mathbb{R}$ and $\lim_{x\to \infty}f'(x)=M$. Show that $\lim_{x\to \infty}f(x+1)-f(x)$ exists and find it. I've been stuck on this question for a long time now and was wondering if anyone could show me how it's done. So far I have done the following: Since $\lim_{x\to \infty}f'(x)=M$ then $\forall \epsilon ,\exists A &gt;0$  s.t. if $x&gt;A$ then $|f'(x)-M|&lt;\epsilon$. So we have that $M-\epsilon&lt;f'(x)&lt;M+\epsilon$. By MVT on $[x,x+1]$ for $x&gt;A$, $\exists c\in (x,x+1)$ s.t. ${f(x+1)-f(x)\over 1}=f'(c)$. Therefore, $M-\epsilon&lt;f(x+1)-f(x)&lt;M+\epsilon$. However, I do not know what to do after this. Using Gimp to batch convert images to another format in Windows As implied by the title, does anybody know how to use the gimp-console-[version].exe program to batch convert images between formats (with default settings) in Windows ? Multiple regression or partial correlation coefficient? And relations between the two I don't even know if this question makes sense, but what is the difference between multiple regression and partial correlation (apart from the obvious differences between correlation and regression, which is not what I am aiming at)?  I want to figure out the following: I have two independent variables ($x_1$, $x_2$) and one dependent variable ($y$). Now individually the independent variables are not correlated with the dependent variable. But for a given $x_1$ $y$ decreases when $x_2$ decreases. So do I analyze that by means of multiple regression or partial correlation?  edit to hopefully improve my question: I am trying to understand the difference between multiple regression and partial correlation. So, when $y$ decreases for a given $x_1$ when $x_2$ decreases, is that due to the combined effect of $x_1$ and $x_2$ on $y$ (multiple regression) or is it due to removing the effect of $x_1$ (partial correlation)? App question timer shouldn't kick in until submission I attempted to ask a question using the iOS app, but it was rejected due to lack of a required tag. On adding the tag I found that I wasn't permitted to submit the question for another 60 seconds, even though this wasn't a new question.  Is this timer intentional, or should it not kick in for edits of questions not actually accepted by the site? MySQL: LEFT JOIN not working as expected Align Caption to the left Can you reuse marinade used with raw chicken? I am little confused with the applicability of reinterpret_cast vs static_cast. From what I have read the general rules are to use static cast when the types can be interpreted at compile time hence the word static. This is the cast the C++ compiler uses internally for implicit casts also.  reinterpret_casts are applicable in two scenarios:   convert integer types to pointer types and vice versa  convert one pointer type to another. The general idea I get is this is unportable and should be avoided.     Where I am a little confused is one usage which I need, I am calling C++ from C and the C code needs to hold on to the C++ object so basically it holds a void*. What cast should be used to convert between the void * and the Class type?  I have seen usage of both static_cast and reinterpret_cast? Though from what I have been reading it appears static is better as the cast can happen at compile time? Though it says to use reinterpret_cast to convert from one pointer type to another? Fancy Chapter Headings Style I would like make a fancy chapter like the figure.    However, i made this code  \documentclass[12pt,a4paper]{book}   \usepackage{lmodern} \usepackage{titlesec} \usepackage{microtype} \usepackage{tikz}    \titleformat{\chapter}[display]   {\normalfont\bfseries\color{black}}   {%\filleft%     \begin{tikzpicture}     \node[       outer sep=-10pt,       text width=2.5cm,       minimum height=3cm,       fill=black,       font=\color{white}\fontsize{80}{90}\selectfont,       align=center       ] (num) {\thechapter};     \node[       rotate=0,       anchor=south,       font=\color{black}\Large\normalfont       ] at ([yshift=43pt,xshift=30]num.west)  {\textls[180]{\textsc{\chaptertitlename}}};       \end{tikzpicture}%  }    {-90pt}   {\titlerule[2.5pt]\vskip3pt\titlerule\vskip4pt\LARGE\sffamily \raggedright }    \begin{document} \chapter{The Singular Sturm-Liouville Problems in Spectral Parameter}    \end{document}      that produces this one    How can I produce the chapter like the First Figure? What is batch size in neural network? I'm using Python Keras package for neural network. This is the . Is batch_size equals to number of test samples? From Wikipedia we have  information:     However, in other cases, evaluating the sum-gradient may require   expensive evaluations of the gradients from all summand functions.   When the training set is enormous and no simple formulas exist,   evaluating the sums of gradients becomes very expensive, because   evaluating the gradient requires evaluating all the summand functions'   gradients. To economize on the computational cost at every iteration,   stochastic gradient descent samples a subset of summand functions at   every step. This is very effective in the case of large-scale machine   learning problems.   Above information is describing test data? Is this same as batch_size in keras (Number of samples per gradient update)? I am pretty sure that most of us here, or at least those do graphic design for living, have found themselves in following situation:   You agree with a client to do the design, agree on price, schedules, formats etc… You work hard, make adjustments, collaborate with client; everything goes well in the beginning. At some point you realise that the client does not listen your professional advice regarding design and prefers his/her own ideas that might not look so professional (choice of fonts, colors, odd choices of elements, shapes etc…). No matter how hard you try, the client is persistent and will not accept the designer’s advice. You get back to work, try to make the best out of it, and the final result is not so good, mainly because you had to stick to the client’s wishes. Work is shipped, payment done, and you don’t want to include this work in your portfolio because it is not good. After all, it is not your work, it is something that was physically created by you as a designer, but the ideas, concept, story, and message came out as a result of nonprofessional person, your client.   Ok, they pay for it, and as long as they are happy this is fine. But, the more compromises you make, the more time you spend working on bad design. If you are a young designer on a quest to get recognition, you don’t want to work just for the sake of money and then face the lack of good design in your portfolio.   Maybe at the beginning of your career you don’t care that much, but later if life this might be a big issue. At some point you will be approached by a big client that might offer you long-term contract, but first they will want to see your work. No point explaining to them what you did and why you made so many compromises.   They will not be interested in that.  Every project is precious as your time and you want to do use it wisely and produce great work.   How would you deal with such a situation? Intuitive explanation for density of transformed variable? Suppose $X$ is a random variable with pdf $f_X(x)$. Then the random variable $Y=X^2$ has the pdf   $$f_Y(y)=\begin{cases}\frac{1}{2\sqrt{y}}\left(f_X(\sqrt{y})+f_X(-\sqrt{y})\right) &amp; y \ge 0 \\ 0 &amp; y \lt 0\end{cases}$$   I understand the calculus behind this. But I'm trying to think of a way to explain it to someone who doesn't know calculus. In particular, I'm trying to explain why the factor $\frac{1}{\sqrt{y}}$ appears out front. I'll take a stab at it:  Suppose $X$ has a Gaussian distribution. Almost all the weight of its pdf is between the values, say, $-3$ and $3.$ But that maps to 0 to 9 for $Y$. So, the heavy weight in the pdf for $X$ has been extended across a wider range of values in the transformation to $Y$. Thus, for $f_Y(y)$ to be a true pdf the extra heavy weight must be downweighted by the multiplicative factor $\frac{1}{\sqrt{y}}$  How does that sound?  If anyone can provide a better explanation of their own or link to one in a document or textbook I'd greatly appreciate it. I find this variable transformation example in several intro mathematical probability/stats books. But I never find an intuitive explanation with it :( I submitted a manuscript last year to an IEEE journal, and the paper was accepted for publication. I recently submitted a new manuscript to the same journal, but, this time, the paper was rejected, and I was told that I should submit to another journal since my paper was not within the journal's scope. The two papers both target similar applications. Furthermore, the second paper uses some work in the first paper, making substantial improvements at solving a much more difficult problem. Based on the reviewer's comments (and my own personal assessment), I do not believe that the work presented in the second paper was "incremental" in nature. Far from it. Two of the three reviewers gave positive reviews. The third reviewer, however, mentioned the "outside of journal's scope" issue and the associate editor and editor-in-chief both sided with the 3rd reviewer, and the paper was stopped dead in its tracks.  I'm scratching my head trying to come to terms with how in the world my first paper could be accepted by this journal, but the second paper focused on the same application space and achieving substantial improvements on a much more difficult problem (backed up with measured results) could be rejected. Any ideas? How to check if this limit exists: $$\lim_{(x,y)\rightarrow (0,0)}{ \frac{x^4y^4}{(x^2 + y^4)^3}}$$  Can I convert it to polar form ? $$\frac{r^8 (\cos^4 (\theta)\sin^4(\theta)}{r^6 (\cos^6 (\theta) + r^6 \sin^{12} (\theta))} = \frac{r^2}{\cos^6(\theta) + 0} = 0$$ Testing Whether a Binomial Distribution Fits Data I have a sample from a discrete distribution as such:   Type:          0   1   2   3   4   5     Occurrences:  88  12  52  43  21   5   My task is to test whether or not a Binomial Distribution (n=5,p) fits this data.   I understand that I'm meant to use hypothesis testing, and that the chi-square test is a staple for this sort of task. I looked at  but I'm still not sure how to set up the test. How do I do this? Evaluate the integral: $\int_{0}^{1} \frac{\ln(x+1)}{x^2+1} \mathrm dx$ How to install specific Ubuntu packages, with exact version? Is there a pattern to which Star Trek ships get the definite article? Some ships in Star Trek are referred to with definite articles. "The Enterprise", "The Defiant". Other ships are referred to without them. "Voyager", "Enterprise". Is there a pattern to or explanation for this behavior? I am carrying out research to look at differences in fish density and fish species richness when using two different underwater visual census methods. My data was originally count data but then typically this is changed to fish density but I have still decided to use a Poisson GLM, which I hope is right.   model1 &lt;- glm(g_den ~ method + site + depth, poisson)   My 3 predictor variables are method, site and depth which I ordered as factors when I input them.   My response variables are grouper species richness, grouper density and the same for other fish groups. I am aware that density is not an integer and it is numerical data e.g 1.34849. I am now however getting this error:      In dpois(y, mu, log = TRUE) : non-integer x = 0.037500   I've been reading up and many people suggest using an offset, is this the most advisable thing to do? Method defined as testMethod do not support web service callouts, test skipped