Intuitively, I know $[f(x)]^2\ge0$ so the integral would be the area above the x-axis and it would result in $[f(x)]^2=0$ and then $f(x)=0$.  How do I prove this with proper terms. This is a reimann integral.
I am working on a few examples where my author said this is true if $h$ is continuous. Can someone explain why? Just because the integral is $0$ doesn't mean the integrand is zero as well.   $\int_{a}^b h^2=0\implies h=0$?
Let $\,f : \mathbb{R} \rightarrow \mathbb{R}$ be a infinitely differentiable function that is  increasing and bounded. Then is it true that $\lim_{x\to \infty}f'(x)=0$? Examples of PCA where PCs with low variance are "useful" Prove that $E$ is disconnected iff there exists two open disjoint sets $A$,$B$ in $X$ Allowing FTP access to a local user without allowing SSH/command line access I'm colorizing the header of a table formatted with column -ts $'\t'  Works well without color codes, but when I add color codes to the first line column doesn't properly align the output.  Without colored output it works as expected: printf "1\t2\t3\nasdasdasdasdasdasdasd\tqwe\tqweqwe\n" | column -ts $'\t'  But when adding color on the first line column doesn't align the text of the colored row: printf "\e[7m1\t2\t3\e[0m\nasdasdasdasdasdasdasd\tqwe\tqweqwe\n" | column -ts $'\t'  Observed this behaviour both on Ubuntu Linux and Mac OS X. How to upload string as file with jQuery or other js framework cgi and tomcat im trying to run a cgi script (.cgi) with tomcat. I am getting the below error and cant find out whats wrong. I know i should really use apache and mod proxy but this really isnt my area of expertise so im taking the easy way out!  Thanks for any help.   java.io.IOException: Cannot run program "perl" (in directory "C:\Java\tomcat\webapps\my_app_name\WEB-INF\cgi"): CreateProcess error=2, The system cannot find the file specified     java.lang.ProcessBuilder.start(ProcessBuilder.java:459)     java.lang.Runtime.exec(Runtime.java:593)     java.lang.Runtime.exec(Runtime.java:431)     org.apache.catalina.servlets.CGIServlet$CGIRunner.run(CGIServlet.java:1705)     org.apache.catalina.servlets.CGIServlet.doGet(CGIServlet.java:597)     javax.servlet.http.HttpServlet.service(HttpServlet.java:627)     javax.servlet.http.HttpServlet.service(HttpServlet.java:729)     org.tuckey.web.filters.urlrewrite.UrlRewriteFilter.doFilter(UrlRewriteFilter.java:738)     org.apache.struts2.dispatcher.FilterDispatcher.doFilter(FilterDispatcher.java:416) Why does Hermione say she hadn't used a memory charm before? After the wedding, Hermione has to use a memory charm on two Death Eaters, where she states that she has never done it before, but she knows the theory. However, she states that before she left on her adventure, she made her parents forget her, and move to Australia. Is this a contradiction, or is there an explanation? I would like to clarify the differences between by value and by reference.  I drew a picture     So, for passing by value,  a copy of an identical object is created with a different reference, and the local variable is assigned the new reference, so to point to the new copy  How to understand the words: " If the function modifies that value, the modifications appear also within the scope of the calling function for both passing by value and by reference "  Thanks! How do I change a user name in Windows 7? Magic quotes in PHP According to the , in order to make code more portable, they recommend using something like the following for escaping data:  if (!get_magic_quotes_gpc()) {     $lastname = addslashes($_POST['lastname']); } else {     $lastname = $_POST['lastname']; }   I have other validation checks that I will be performing, but how secure is the above strictly in terms of escaping data? I also saw that magic quotes will be deprecated in PHP 6. How will that affect the above code? I would prefer not to have to rely on a database-specific escaping function like mysql_real_escape_string(). Is there a way to get reverse numbering on the enumerate environment? To build a list of publications, I wish to show the most recent on top of the list, while keeping the numbering similar. This can be achieved manually by doing something like:  \begin{enumerate} \item[42] pub num 42 \item[41] pub num 41 \item[...] \item[1] pub num 1 \end{enumerate}   but is there a more principled approach? $\forall x,y>0, x^x+y^y \geq x^y + y^x$ Prove that $\forall x,y&gt;0, x^x+y^y \geq x^y + y^x$   A friend of mine told me none of the teachers in my school have succeeded in proving this seemingly simple inequality (it was asked at an oral exam last year). I tried it myself, but I made no significant progress. How soon should I "vote to close"? My keyboard is typing by itself, could there be a ghost in it? For integers $a$ and $b$, $ab=\text{lcm}(a,b)\cdot\text{hcf}(a,b)$ I was reading a text book and came across the following:  Important Results (This comes immediately after LCM:) If 2 [integers] $a$ and $b$ are given, and their $LCM$ and $HCF$ are $L$ and $H$ respectively, then $L \times H = a \times b$  Can some please help me understand why the above result is true? Thanks in advance. What autofocus zone selection mode should I use for action/event shooting? I have a Canon 7D, and typically shoot everything I do in its single-point autofocus zone select mode, because I usually want fine control over exactly what the camera is focusing on and I often find that its two automatic focus zone select modes don't focus on what I want in focus.  For most of the photography I do, this is fine -- I have enough time that I can compose the shot the way I want, use the joystick on the back to select the right focus point, and take the shot at my leisure.  However, recently I've been doing more event/action photography, and I've been running into issues with this mode of operation.  Too often, I will see a person start to do something interesting, but my autofocus point is not in the right place -- so by the time I get the camera up, adjust the settings, and move the autofocus point, the opportunity to take the shot has passed.  My question is, what autofocus zone selection mode and workflow should I use for this type of photography?  I could use the 5-zone partial-auto mode (which gives me a choice of top, middle, bottom, left, or right, and then the camera chooses the points within my selected region), but I find that the time needed to switch in between that mode and the single-point mode is similarly prohibitive, and I have to hope that the camera chooses the right thing to focus on. Solve the recurrence $T(n) = 2T(n-1) + n$ Why does the x86-64 / AMD64 System V ABI mandate a 16 byte stack alignment? How does Latex compilers integrate packages into its existing core functions?