Given that $f(x)$ is continuous on $[0,\infty]$.  If $\lim\limits_{x\to\infty}\left(f(x)+\int_{0}^xf(t)dt\right)$ exists   then evaluate $\lim\limits_{x\to\infty}f(x)$
I want to prove or disprove this problem: If there exist $\lim\limits_{x\rightarrow \infty} (f'(x)+f(x))=L&lt;\infty$ then $\lim\limits_{x\rightarrow\infty} f(x) =L$.  When I assume problem below:  If there exist $\lim\limits_{x\rightarrow\infty} (f'(x)+f(x)) =L&lt;\infty$, There exists $\lim\limits_{x\rightarrow\infty} f(x)$?  I can use mean-value theorem to show that.  So my question is:     If $\lim\limits_{x\rightarrow\infty} (f'(x)+f(x))=L&lt;\infty$, does $\lim\limits_{x\rightarrow\infty} f(x)$ exist?
Blackboard bold characters The blackboard bold font in the AMSFonts package only has capital letters.  I sometimes wish to use a blackboard bold "1", for which I can use \usepackage{bbold}. But this changes the entire blackboard bold font, and I like the original AMSFonts versions of the capital letters better.  Is there a simple way for me to get \mathbb{1} from one package and the blackboard bold capitals from another? Natbib puts reference data one line per item I'm using:  \documentclass[oneside,article,openbib,12pt,titlepage]{memoir} \usepackage[authoryear,round]{natbib} % Better bibliography support \bibpunct{(}{)}{,}{a}{,}{,}   in the preamble of my document and  \backmatter \renewcommand{\bibname}{References} \bibliographystyle{chicago}    \bibliography{listb,mybib}   in the body of the file. But a typical formatted reference is:     Freely, I. (1997).   A small paper.   The journal of small papers -1. to appear.   I've tried other non-natbib styles (e.g., regstud), and the reference flows and wraps as it should. So how does one get natbib to do the same?  Also, how does one get natbib to include the authors' entire first names? Concatenating two std::vectors What is a good method for short text clustering? I am working on a text clustering problem. The data contains several sentences. Is there a good algorithm which reaches high accuracy on short text?  Can you provide good references?   Algorithms such as KMeans, spectral clustering does not work well for this problem. Item cannot be installed or removed until the package catalogue is repaired How do I reset a lost administrative password? I'm working on a Ubuntu system, and my client has completely forgotten his administrative password. He doesn't even remember entering one; however it is there.  I've tried the suggestions on the website, and I have been unsuccessful in deleting the password so that I can download applets required for running some files. Is there a solution? Jet stream of water I would like to simulate a stream of water like the one in the picture, but I don't know how to simulate the fast-moving, white water. Should I use particles to simulate foam or is it much better to concentrate in the material properties? Thanks How to convert a 3 column csv file into a table (or matrix) I have an CSV input file format like this, with a nucleotide sequence in field 1, text in field 2, and an integer in field 4:  ATGC,CD3,56 ATGC,CD4,67 ATGC,IgD,126 ATGC,IgM,127 AGTC,CD3,67 AGTC,CD4,78 AGTC,IgD,102 AGTC,IgM,89 TCGA,CD3,334 TCGA,CD4,123 TCGA,IgD,456 TCGA,IgM,80 CGTA,CD3,54 CGTA,CD4,32 CGTA,IgD,82 CGTA,IgM,117   I opened this CSV file using Numbers in Mac it's display as 3 columns format, however, I want to convert it to the table(or Matrix) format (also a CSV file), making the first column, the nucleotide sequences, into a header, and want the result to also look like a table (or Matrix):       ATGC  AGTC  TCGA  CGTA CD3  56    67    334   54 CD4  67    78    123   32 IgD  126   102   456   82 IgM  127   89    80    117   Below is a section from my real input CSV file (sample input.txt):  AGAATAGTCTGATTCT,-,,38 AGAATAGTCTGATTCT,AnnexinV,,51 AGAATAGTCTGATTCT,CD127,,39 AGAATAGTCTGATTCT,CD138,,3 AGAATAGTCTGATTCT,CD14,,2 AGAATAGTCTGATTCT,CD16,,4 AGAATAGTCTGATTCT,CD19,,10 AGAATAGTCTGATTCT,CD20,,6 AGAATAGTCTGATTCT,CD24,,21 AGAATAGTCTGATTCT,CD25,,4 AGAATAGTCTGATTCT,CD27,,87 AGAATAGTCTGATTCT,CD3,,235 AGAATAGTCTGATTCT,CD34,,5 AGAATAGTCTGATTCT,CD38,,18 AGAATAGTCTGATTCT,CD4,,412 AGAATAGTCTGATTCT,CD43,,99 AGAATAGTCTGATTCT,CD5,,430 AGAATAGTCTGATTCT,CD56,,3 AGAATAGTCTGATTCT,CD8,,7 AGAATAGTCTGATTCT,IgD,,4 AGAATAGTCTGATTCT,IgM,,2 TGTGGTAGTTCGTCTC,-,,9 TGTGGTAGTTCGTCTC,AnnexinV,,42 TGTGGTAGTTCGTCTC,CD127,,6 TGTGGTAGTTCGTCTC,CD138,,4 TGTGGTAGTTCGTCTC,CD16,,40 TGTGGTAGTTCGTCTC,CD19,,7 TGTGGTAGTTCGTCTC,CD20,,2 TGTGGTAGTTCGTCTC,CD24,,24 TGTGGTAGTTCGTCTC,CD25,,2   How can I do this using Linux text formatting commands? How to concatenate multiple lines of output to one line? Making a 3D map with shapefiles, lidar and aerial image data I want to try to make a simple 3D map for a small area (10 square miles) with some housing, some roads and some vegetation on it. My geodata is as follows:    shapes with houses/roads/vegetation.  LIDAR point cloud data over the area (can easily be built to a dem). georeferenced aerial image.   Any idea where to start to bundle these geodata together and make a neat looking 3D map? How do you send a HEAD HTTP request in Python 2? What I'm trying to do here is get the headers of a given URL so I can determine the MIME type. I want to be able to see if http://somedomain/foo/ will return an HTML document or a JPEG image for example. Thus, I need to figure out how to send a HEAD request so that I can read the MIME type without having to download the content. Does anyone know of an easy way of doing this? Why uniform closure $\mathscr{B}$ of an algebra $\mathscr{A}$ of bounded complex functions is uniformly closed? Let $\mathscr{A}$ be an algebra of bounded complex functions. (Or if necessary, continuous and domain of functions is compact)  Definition:  $\mathscr{B}$ is uniformly closed iff $f\in\mathscr{B}$ whenever $f_n\in \mathscr{B} (n=1,2,\cdot)$ and $f_n\rightarrow f$ uniformly.  $\mathscr{B}$ is the uniform closure of $\mathscr{A}$ iff $\mathscr{B}$ is the set of all functions which are limits of uniformly convergent sequences of members of $\mathscr{A}$.  ============  Let $\mathscr{B}$ be a uniform closure of $\mathscr{A}$.  How do i prove that $\mathscr{B}$ is uniformly closed in ZF?  Does Stone-Weierstrass theorem require choice since it is critical to prove Stone-Weierstrass Theorem? What lens focal length most closely resembles the perspective of the human eye? How to Delete Elements from List1 appearing in List2? How to link processing power of old computers together? Why do German umlauts and sharp s (ß) work without a package in LaTeX? I am used to the fact that LaTeX will only know letters like ä, ö, ü, or ß if I use packages like  \usepackage{ucs} \usepackage[utf8x]{inputenc} \usepackage[T1]{fontenc}   Today, I tried LaTeX on a Mac for the first time, using the MacTeX distribution and texmaker. Without writing down any packages, all umlauts and ß were accepted correctly from scratch. Why is that and will the usage of special letters without using the packages cause any problems? Abandoned colony of military engineer corps Can we simulate the whole universe in computer? Here is an idea: As human kind we discovered many laws, formulas, events, etc. in our surrounding environment.here is a way to discover the unknowns :   Now if we simulate a virtual world with our knowledge in computers we expect it to work, because we guess that we know all of it. If a bug occurs in the simulation or something acts differently from the expected in the real world, that may tell us that there is something new; a thing (law, formula, ...) that we didn't know, which causes that bug or that anomaly.  For examples imagine that we created a virtual simulation for motion dynamics and we didn't add the friction to our simulation. Everything in the simulation will work fine but in a different manner. So if we hadn't discovered friction yet, would it help us to think about if there is something we didn't add? Or if there is something we don't know?       But can we simulate the whole universe, everything we know, in one simulation? I know it will require a deadly high computational power. Something like what they did for DNA; two years of computation to analyse their pattern. can we simulate everything we know to create a virtual universe to compare it to our real universe? Google Sheets has several import functions   IMPORTDATA IMPORTFEED IMPORTHTML IMPORTXML   Sometimes the above functions returns errors like #N/A Imported content is empty and would like to be sure that there isn't a problem with the resource content to be imported.  How do I know if these functions are able to get the content that I looking to import?  I know that there also exist IMPORTRANGE but that function only is able to import content from Google Sheets spreadsheets What does if __name__ == "__main__": do? Given the following code, what does the if __name__ == "__main__": do?  # Threading example import time, thread  def myfunction(string, sleeptime, lock, *args):     while True:         lock.acquire()         time.sleep(sleeptime)         lock.release()         time.sleep(sleeptime)  if __name__ == "__main__":     lock = thread.allocate_lock()     thread.start_new_thread(myfunction, ("Thread #: 1", 2, lock))     thread.start_new_thread(myfunction, ("Thread #: 2", 2, lock))