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We are asked the following:      let $f(x)$ be a continuous function on $[0, 1]$ such that   $$\int _ {0} ^ {1} \ f(y) dy = 1$$   prove that $f(x) = 1$ for some $x ∈ [0, 1]$   The question asks to take into account Rolle's Theorem and Mean Value Theorem.  I'm aware of the definitions, but I am really unsure how to answer this question and my tutors are not really responding till after easter.    Could someone please help? Why is there a "y" involved?  Thanks you I am trying to integrate one Salesforce org to other org by using Oauth setup, I wanted to use  use consumer key and consumer secret key in my REST class to connect with the org, after connection part completion, I want to access Get(), Put(), Post(), etc. Including the ability to set Oauth and Authorization headers needed for Salesforce Rest API calls.  Actually I'm new in REST implementation so can you please explain me by using code samples. I'm interested: What is C#'s analog of std::pair in C++? I found System.Web.UI.Pair class, but I'd prefer something template-based.  Thank you! how to permanently disable ubuntu updates & hide install updates button pic included how to permanently disable ubuntu updates pop up &amp; hide or remove Install Updates button pic included see below: What the #$@&%*! is that called? If a matrix has orthonormal columns, they must be linearly independent, so $A^+ = (A^T A)^{−1} A^T$ . Also, the fact that its columns are orthonormal gives $A^T A = I$. Therefore,  $$A^+ = (A^T A)^{−1} A^T = (I)^{-1}A^T = A^T$$  Thus, $A^+ = A^T$. Am I correct? Thank you. Regulated AC power supply? What's the difference between iterating over a file with foreach or while in Perl? Why I think tension should be twice the force in a tug of war I'm going to provide my argument for why I think the tension in a rope should be twice the force exerted on either side of it.  First, let's consider a different example. Say, there is a person named A and a block in space. A pushes on the block with a force of 100 N. Then, the block will also push A with a force of 100 N by Newton's third law. Now, consider the case where instead of the block, there is a person B who is also pushing on A with a force of 100 N while A is pushing on him. A will experience a force of 100 N because he pushed on B, AND another 100 N because he is being pushed by B. Hence he will experience a force of 200 N. Similarly, B also experiences 200 N of force.  Now, back to the original problem. There are two people A and B in space with a taut rope (no tension currently) in between them. If only A is pulling and B is not, then I agree that the tension is equal to the force A exerts. This situation (in my opinion) becomes analogous to the above if B is also pulling. So, say both of them pull from either side with a force of 100 N. Then the rope at the end of B will pull B with a force of 100 N (this pull is caused by A). By Newton's third law, the rope will experience a pull of 100 N. But B is also pulling his end of the rope with 100 N. Therefore, the tension should be 200 N. Similarly, the end of the rope at A must pull A with 100 N of force (because B is pulling from the other side) and hence experience a force of 100 N itself by Newton's third law plus another 100 N because A is pulling on the rope.  Apparently, the answer is not this (according to my searching on the web). So, could anyone tell me why this reasoning is wrong? Thanks.  EDIT : So apparently people don't agree with my first example, leave alone the second. This is to the downvoters and the upvoters of the highest-rated answer: You all agree that if only A pushes B with a force of 100 N, then A and B both will get pushed by a force of 100 N in opposite directions, right? Then, in the case where B is also pushing with a force of 100 N, it doesn't make sense that the answer would be exactly the same. It doesn't seem right that no matter what B does, B and A will always experience the same force as they would have if B hadn't applied any force.  EDIT 2 : I'm going to provide here a link to a question that I posted:  According to the answer and the comments there, the reason as to why my first example is incorrect is different to the one provided here. So maybe you should all read the answer and the comments provided by the person and reconsider what you think. Product of manifolds & orientability I was writing test classes for my apex Rest Service that I had built for an Ipad app.  I noted some very interesting things while experimenting. Before doing anything, I just did a google search and found an interesting blog post by Jeff.    @RestResource(urlMapping='/v.9/member/*/results/*')  global with sharing class MemberRestSvc {  @HttpGet  global static ReturnClass doGet() {  String[] uriKeys = RestContext.request.requestURI.split('/'); // get the member name from the uri String memberName = uriKeys.get(uriKeys.size()-3);  // do awesome programming stuff here &amp; catch any exceptions try {    List&lt;Contact&gt; contacts = [Select Id From Contact where member_name__c = :memberName];   return new ReturnClass('true', 'Query executed successfully.', contacts);  } catch (Exception e) {   return new ReturnClass('false', e.getMessage(), null); }   }   global class ReturnClass {  global String success; global String message; global List&lt;Contact&gt; records;    global ReturnClass(String success, String message, List&lt;Contact&gt; records) {   this.success = success;   this.message = message;   this.records = records;  }  }  }   And here is the test class  @isTest private class Test_MemberRestSvc {  static { // setup test data   }  static testMethod void testDoGet() {  RestRequest req = new RestRequest();  RestResponse res = new RestResponse();  req.requestURI = 'https://cs9.salesforce.com/services/apexrest/v.9/member/me/results/today';   req.httpMethod = 'GET'; RestContext.request = req; RestContext.response = res;  MemberRestSvc.ReturnClass results = MemberRestSvc.doGet();  System.assertEquals('true', results.success); System.assertEquals(10, results.records.size()); System.assertEquals('Query executed successfully.', results.message);  }  }   I just commented a few lines and ran and it. I still achieved enough test coverage so my question is why do I need to simply instantiate the Rest request and response objects since I am directly calling the class?    @isTest   private class Test_MemberRestSvc {    static {     // setup test data     }  static testMethod void testDoGet() {  /*RestRequest req = new RestRequest();  RestResponse res = new RestResponse();  req.requestURI =    'https://cs9.salesforce.com/services/apexrest/v.9/member/me/results/today';   req.httpMethod = 'GET'; RestContext.request = req; RestContext.response = res; */Commented the code meant for REST apex intialization and merely calling the method!!  MemberRestSvc.ReturnClass results = MemberRestSvc.doGet();  System.assertEquals('true', results.success); System.assertEquals(10, results.records.size()); System.assertEquals('Query executed successfully.', results.message);  }  }   Can someone explain this behavior? Also what are the best practices for writing Test classes for apex Rest services? I put all my music on a playlist seperate from the rest of the music on the iTunes library, so I could easily get to what music I wanted to listen to, instead of my brother or sister's music. My brother recently got an iPod nano, and didn't know how to use iTunes, after explaining it to him, he deleted my whole entire playlist. I didn't know, so when I hooked my phone up to the computer to sync some songs I was going to buy, all the music on my phone disappeared. I've tried re-doing the playlist and syncing all of it to my phone again, but it won't work. I've also tried turning off my phone for certain periods of time, still nothing.  I lost about 200 songs (thankfully not more), and I don't know how to get it back. How to treat English questions which have code in a foreign language? After creating some hi-poly model, i'm always creating low-poly model by approximating that hi-poly mesh with triangle-by-triangle LP mesh - with snap to face mode turned on.   So the process looks like CTRL + RMB (x times), and hitting F on keyboard, so the new face was made.  Then I'm using this low poly model to texture baking, mainly for gamedev purposes.  This method is very time consuming, so how to make retopology process easier and quicker? Pearson VS Deviance Residuals in logistic regression I know that standardized Pearson Residuals are obtained in a traditional probabilistic way: $$ r_i = \frac{y_i-\hat{\pi}_i}{\sqrt{\hat{\pi}_i(1-\hat{\pi}_i)}}$$ and Deviance Residuals are obtained through a more statistical way (the contribution of each point to the likelihood): $$ d_i = s_i \sqrt{-2[y_i \log \hat{\pi_i} + (1 - y_i)\log(1-\hat{\pi}_i)]} $$ where $s_i$ = 1 if $y_i$ = 1 and $s_i$ = -1 if $y_i$ = 0. Can you explain to me, intuitively, how to interpret the formula for deviance residuals? Moreover, if I want to choose one, which one is more suitable and why? BTW, some references claim that we derive the deviance residuals based on the term $$-\frac{1}{2}{r_i}^2$$ where $r_i$ is mentioned above. "grey" vs "gray" are both common equally in use? Yesterday I wrote "gray" in the meaning of the color, but my friend corrected me and told me to write "grey". Today I checked in the  and I found that they are both correct for the same meaning. So, now I just have doubt which one of them is more common in use. How do I find a point a given distance from another point along a line? What is the difference between local and global sequence alignments? There are a bunch of , and I don't want to get bogged down in the maths behind them as this not only between software but varies from software version to version.  There are two main divides in the programs; some use local alignments and others use global alignments. My question is threefold:   What are the fundamental differences between the two? What are the advantages and disadvantages of each? When should one use either a global or local sequence alignment? I tried out several image editors mentioned on  but some of them (like  and ) were very disappointing. These apps were too simple and low level.  What do you suggest for a (preferably free) image editor on OS X?  P.S: I was using  on Linux and also know that it was released for OS X too, but I want to find new good applications. I am starting to learn some Regex, therefore I use this command repeatedly:  grep pattern /usr/share/dict/american-english    Only the part with pattern changes, so I have to write the long expression "/usr/share/dict/american-english" again and again.   Someone made the remark that it is possible to expand an argument of a command from the command history by typing cryptic character combinations instead of the full expression.  Could you tell me those cryptic character combinations ?