let two function $f(x),g(x):[0,1]\to [0,1]$ are Continuous function,and $f(x)$ strictly monotone increasing, show that $$\int_{0}^{1}(f(x)+g(x))dx\ge\int_{0}^{1}f(g(x))dx$$  I am not comfortable with compositions and don't have any idea on how to deal with the problem. Any help will be appreciated. Thanks! This problem is from analysis problem book excises by Min hui xie (This book exsice problem it is very hard)
Suppose $f(x)$ and $g(x)$ are continuous function from $[0,1]\rightarrow [0,1]$, and $f$ is monotone increasing, then how to prove the following inequality: $$\int_{0}^{1}f(g(x))dx\le\int_{0}^{1}f(x)dx+\int_{0}^{1}g(x)dx$$
How do I recover files from an USB flash drive? Possible Duplicate:          I have a USB flash drive that claims it needs to be formatted every time I put it into my computer (Windows).  Yesterday the drive was healthy and had data on it.  The data is probalby still there.  Are there any free tools to restore the drive?  If not free, what tools are known to work in this situation? I am flying to Tbilisi, Georgia with Turkish Airline. My stay in Istanbul is 12 hours. Can I get transit visa to visit Istanbul city ?    I am from Pakistan with Oman employment visa. How to prove $x^{n}$ is not uniformly continuous How to prove $x^{n}$ is not uniformly continuous on the interval $[0, +\infty)$? Exporting QGIS contour attributes in DXF file? I have a .tiff data file that generates contours in QGIS. I save it as .dxf. The contours don't have any attributes or data. That's bad, because I want to make a 3D landscape in Revit using the information.   How do a save/export the contour lines from QGIS so that they have a z-elevation attribute or at least some information?    I ticked the attributes box when extracting the contours, but the attributes doesn't show in the dxf. How can black hole increase its mass? How do I set a static IP address in Windows? Why is feed-forward mechanism used in hash functions? The compression function of SHA-1 when used in Davies-Meyer mode adds its input to the chaining values at the final step. For the first message block, the IV is used as the input and in the next step, the previous block's output (as specified by Merkle-Damgård) is used. These values are fed to the last round of the compression function.  Why would removing the feed-forward part (i.e.,the final step where the input value is added to the result to get the final output) make the hash function insecure? Apart from the fact that the compression function would not satisfy desired randomness properties (being a permutation for each fixed message). Does centrifugal force exist? Currently in my last year of high school, and I have always been told that  does not exist by my physics teachers. Today my girlfriend in the year below asked me what centrifugal force was, I told her it didn't exist, and then she told me her textbook said it did, and defined it as "The apparent force experienced towards the outside of a circle is the centrifugal force and is due to the mass of the object resisting the inward centripetal acceleration that the object is experiencing". I was pretty shocked to hear this after a few years of being told that it does not exist.  I did some reading and found out all sorts of things about pseudo forces and reference frames. I was wondering if someone could please explain to me what is going on? Is it wrong to say that centrifugal force does not exist?   This has always nagged me a bit as I often wonder that if every force has a reaction force then a centripetal force must have a reaction centrifugal force, but when I asked my teachers about this they told me that centrifugal force does not exist. How to fix "Notification access is not available" on Android Go? Paucity of words for relationships Converting a .lasd (Lidar) coordinate system? How can one change a coordinate system for a .lasd (Lidar) dataset?  The file is currently in UTM_Zone_15N and I am trying to convert it to IL_East. Could the missing antimatter lie outside the observable universe? Changing the homepage I have a question related to modeling short time-series. It is not a question , but how. What method would you recommend for modeling (very) short time-series (say of length $T \leq 20$)? By "best" I mean here the most robust one, that is the least prone to errors due the fact of limited numbers of observations. With short series single observations could influence the forecast, so the method should provide a cautious estimate of errors and possible variability connected to the forecast. I am generally interested in univariate time-series but it would be also interesting to know about other methods. How do you make the camera in blender cycles render everything so it looks like pixels? I want everything in my scene to look pixelly like this image I found: I have a requirement for a custom app I am building to open an attachment on the parent record in a new window on create of a child record.  I have parent object Quality_Assessment__c with child object Chart_Review__c. Quality_Assessment__c has a PDF attached to it in the Notes &amp; Attachments section. When a user clicks to create a new Chart_Review__c record I need to have the PDF attachment on the Quality_Assessment__c record open in a new tab as well as the record create page for the Chart_Review__c record. Looking for help in generating the needed javascript for a custom button to accomplish this.  The 'Quality_Assessment__c' record will have a PDF file attached to it prior to the user clicking the 'New Chart Review' button.  My use case is to have users open the 'Quality_Assessment__c' record and perform what we call a Chart Review. To perform the Chart Review the user would click on a custom button called 'New Chart Review' which would do two things.   create a new 'Chart_Review__c' record displaying the new record edit page  open the PDF attachment from the related 'Quality_Assessment__c' record.    Preferably on click of the button the new record page would open in existing tab and a new tab with the PDF would open simultaneously. Can I travel to Croatia with single-entry Schengen visa? I am traveling to Zurich with a single-entry Schengen visa.  While coming back can I travel to Croatia for 3 days and then return to India (Country of Origin)? Do lure modules and incense cause new pokemon to spawn near you, or existing pokemon to be drawn to you? How to merge columns in a table? I have this table, but wanted to format the first row. I like to match the two columns of first row, and last two columns of the same first row. Any suggestion on how to do that?  \begin{table}[!h]  \caption{Comparison of percentages.} \begin{tabular}{lclclclclc} \hline \hline  Mode &amp;  Var  &amp;  Cum\\ \hline {}       &amp; EF   &amp; CHF    &amp; EF2   &amp; CHF2\\ 1   &amp;  17.5 &amp; 19.1   &amp; 17.5  &amp; 19.1\\ 2   &amp;  11.8 &amp; 12.7   &amp; 29.3  &amp;  31.9\\ 3   &amp;  6.6  &amp;  5.6         &amp; 35.9    &amp;  37.4\\ \hline \end{tabular} \end{table} How can I find duplicate photos? What can I use to find duplicate photos, including photos that have been resized?