If $f$ is a continuous function with $\displaystyle \int _{ 0 }^{ x}{  f(t)dt\rightarrow\infty }  $ as $|x|\rightarrow\infty$,then show that    every line      $y=mx$ intersects the curve $\displaystyle y^2+\int _{ 0 }^{ x }{  f(t)dt=2!}  $   I can't understand how to proceed with this problem.Any suggestion?
If $f$ is a continuous function with $\displaystyle \int_{0}^{x}f(t)dt\rightarrow \infty$ as $|x|\rightarrow \infty\;,$ Then show that every line $y=mx$ Intersect the curve $\displaystyle y^2+\int_{0}^{x}f(t)dt=2$  $\bf{My\; Try::}$ Put $y=mx$ in $$\displaystyle y^2+\int_{0}^{x}f(t)dt=2\;,$$ We get $$\displaystyle m^2x^2+y^2+\int_{0}^{x}f(t)dt=2.$$ We can write it as $$\displaystyle 2\int_{0}^{x}2m^2tdt+\int_{0}^{x}f(t)dt=2$$ So $$\displaystyle \int_{0}^{x}\left[2m^2t+f(t)\right]dt-2 =0$$ Now Let $$g(x) = \displaystyle \int_{0}^{x}\left[2m^2t+f(t)\right]dt-2.\;,$$ When $x\rightarrow \infty\;,$ Then $g(x)\rightarrow \infty.$ (Where $g(x)$ is an Continuous function.) Now I did not Understand How can i solve that, Help me Thanks
I've played around in the past of the 2D Flash fan-made version of the popular Valve game Portal.  It has basically the exact same mechanics, but as a 2D side-view flash game.  Lately I've toyed around with creating a simplified flash version of some of my favorite franchises (such as Zelda, Mario, Splinter Cell, etc.).  Of course, nothing is "stopping" me from just using the same mechanics and just changing the name to something not copyrighted.  I have witnessed projects that have tried to directly port a 3D game into a 2D simplified version, with the exact same plot and puzzles (Ocarina of Time in 2D comes to mind), and I have seen them being shut down.  But I am not likely going to exactly duplicate any game...just borrow some of the source material and basic underlying mechanics.  For example, if I were to make a Zelda-influenced fan game, I would have items such as the Hookshot, Boomerang, and all other sorts of ones from the Gameboy Zeldas; just with a custom plot and dungeons.  With likely the same mechanics.  What are the legal issues involved in this?  I used to think it was a "Don't do this ever; it's a bad idea."  But then I've seen the Portal clone, and now I'm curious. Deploy a project using Git push When I have .txt files or .py files, I can Quick Look those files in Finder. I have .jl files that are codes written in the Julia Language. Of course they are text files. They will open in a text editor like Sublime Text. How can I Quick Look these .jl files in Finder? I'm using Dataloader to Upsert a Child Account to Parent Account using an external ID.  When the Upsert is complete, the Child overwrites the parent, it's not not connecting the Child Account to the Parent Account.  ((See Answer Below)) How to prove that we are living in a 3+1D world? I have a Surface Pro 4 and an iMac (late 2019). I would like to connect my Surface Pro to the iMac to use the iMac screen as a second monitor.  Is that possible?  What are the requirements to use an iMac as a second screen? I want to try to convert a string to a Guid, but I don't want to rely on catching exceptions (   for performance reasons - exceptions are expensive for usability reasons - the debugger pops up  for design reasons - the expected is not exceptional   In other words the code:  public static Boolean TryStrToGuid(String s, out Guid value) {     try     {         value = new Guid(s);         return true;     }     catch (FormatException)     {         value = Guid.Empty;         return false;     } }   is not suitable.  I would try using RegEx, but since the guid can be parenthesis wrapped, brace wrapped, none wrapped, makes it hard.   Additionally, I thought certain Guid values are invalid(?)    Update 1   had a good idea to catch only FormatException, rather than all. Changed the question's code sample to include suggestion.    Update 2  Why worry about thrown exceptions? Am I really expecting invalid GUIDs all that often?   The answer is yes. That is why I am using TryStrToGuid - I am expecting bad data.  Example 1 . I might be parsing folder names, checking to see if the text after the final . is a GUID.  c:\Program Files c:\Program Files.old c:\Users c:\Users.old c:\UserManager.{CE7F5AA5-6832-43FE-BAE1-80D14CD8F666} c:\Windows c:\Windows.old   Example 2 I might be running a heavily used web-server wants to check the validity of some posted back data. I don't want invalid data tying up resources 2-3 orders of magnitude higher than it needs to be.  Example 3 I might be parsing a search expression entered by a user.     If they enter GUID's I want to process them specially (such as specifically searching for that object, or highlight and format that specific search term in the response text.)    Update 3 - Performance benchmarks  Test converting 10,000 good Guids, and 10,000 bad Guids.  Catch FormatException:    10,000 good:     63,668 ticks    10,000 bad:   6,435,609 ticks  Regex Pre-Screen with try-catch:    10,000 good:    637,633 ticks    10,000 bad:     717,894 ticks  COM Interop CLSIDFromString    10,000 good:    126,120 ticks    10,000 bad:      23,134 ticks   p.s. I shouldn't have to justify a question. Uniform Scattering with vector I'm attempting to create a random spread of dots to create a gradient look. I'm getting really close to the effect I want by blending two scatter brushes. The issue I'm having is that the blended brushes creates unwanted lines, and the dots run into each other. I keep adjusting the settings with no luck.  Here's the effect I'm wanting to achieved.    Smooth transition  On Circular path Dots don't converge Scattered at random-ish     Here's how close I'm able to get:   Blended scatters create unwanted lines Dots converge Spacing isn't gradual from edge to center What's the intuition behind "stiff systems"? Shortcut for toggling between different windows of same app? I opened two Google Chrome windows (because I am using multiple Gmails) and when I do the Cmd ⌘ Tab ⇥ shortcut it just shows me other applications that I opened but does not show me the other Chrome windows that are already opened.  How to switch to the other Google Chrome window that I opened using keyboard shortcut? I have just migrated from Windows environment. I have installed Python 3.2 in a separate directory. How can I get the python installation path in Ubuntu shell?  Is there any way I can let the shell know/choose at runtime which python version is to be used for further code execution?  Are there any environment variables and search path kind of things in Ubuntu Linux as well? How to see the correctness of close/reopen votes? How can I see the ratio of my previous close/reopen votes that were correct (i.e. resulted in the question being closed/reopened) or incorrect (i.e. resulted in the question left open/closed)?   I am interested in this statistic, because it would help self-educate about the correct use of close/reopen votes. Why is the [I'm Done] button unavailable after only flagging comments in the First Posts review queue? I just flagged two comments during a review of a question in the First Posts queue (on another SE site). Then I wanted to select the button I'm Done, but it's unavailable (I can only select No action needed). Even if I refresh my page (while still on that review page), it remains the same.  If however I also downvote the question (only temporary, as a test, since I don't want to downvote the question being reviewed), then it seems to work as I'd expect it to: the button I'm Done becomes available, and No action needed becomes unavailable.  Why is the I'm Done button unavailable after only flagging comments in the First Posts review queue?  Notes:   I'm not convinced that you're supposed to review the actual post, and not (only) the comments underneath it (as mentioned in 's comment). Because "if" I would post a new comment, or just upvote an existing comment, I can actually select I'm Done. While in this case I flagged existing comments which IMO had become obsolete. Flagging comments is "acting on comments". And if my flag gets accepted (in this case: "no longer needed"), and the comment is actually deleted (by the mod), then it makes the question a bit more readable (= don't waste your time digesting a comment which is obsolete). Therefor "IMO", in the end I also "acted on the post". Think about all those posts with a zillion of comments, of which many are obsolete (e.g because the post got updated already). I am not sure (yet) if a similar issue exist in any other review queue (i.e. the Late Answers queue). How to show $u \in R^{x} \implies u \in R[X]^{x}$ for integral domain $(R,+, \times)$ Cannot expand asterisk without proper permission Two Answers, One Question Sometimes, when I answer a question on Stack Overflow, I have two different answers that are equally valid. This happens most when answering architectural questions where there are many valid ways to solve a problem.  Is it better to put each alternative into a single answer, or put each alternative in its own answer?  Posted each alternative separately will allow the voting system to float the best answer to the top, but I don't want to be accused of rep whoring by "flooding" a question with answers.  What's your opinion? One or two answers? How do you read C declarations? I have heard of some methods, but none of them have stuck. Personally I try to avoid complex types in C and try to break them into component typedef.  I'm now faced with maintaining some legacy code from a so called 'three star programmer', and I'm having a hard time reading some of the ***code[][].  How do you read complex C declarations? Quantum mechanical books for mathematicians I'm a mathematician. I have good knowledge of superior analysis, distribution theory, Hilbert spaces, Sobolev spaces, and applications to PDE theory. I also have good knowledge of differential geometry. I would like to study the Semiclassic Analysis, but perhaps I must first study the foundations of quantum mechanics. So I would like to know what book you recommend me to begin studying quantum mechanics. I'm primarily interested in a mathematical point of view. I have seen some books of this type, but I would like to have some other opinion.  Thanks for every reply gdal_translate- why jpg compressed tif is 2 times greater than jpg file? Was just wondering if there is any solid data available as to how many people are using ubuntu. I was also interested in the attrition rate with ubuntu users, etc.