KEYMACRO is an Open Source application that allows you to configure Macro Button on your keyboard. You can use it to record text or your movements. Just remember the two items:
1. SET UP YOUR CUSTOM MAPPING!
In order to make your Keys work the way you want them to work, you’ll need to configure your own mapping. Find out more about that in the APP.
2. USING THE KEYMACRO APP
Simply click on the ‘Record Me’ button to begin recording. You can then set a time limit and even add a countdown timer.
Once you’re done recording, simply click on the ‘Stop’ button to stop recording. Now you just need to convert the.3D key to a graphic by clicking on ‘Convert Me’.
Finally, simply play it back by clicking on ‘Recorded’.
Keymacro only works on the following keyboards:
• MagicMouse™
• MagicScribe™
• Topre Mechanical Keyboard™
You can find out more about the applications features at the app’s website:
Sleek and clean user interface
The application doesn’t take long to install and it doesn’t come with a complicated setup that you would need to complete before you can actually use it. It sports a clean and intuitive graphical interface with many nice tools at hand.
Cheetah Video Converter is a nice software solution that allows you to convert various files and videos into multiple formats, it can edit the video length and adjust some options.
Convert various files easily
The first thing that you need to do after launching the application is to browse your computer and add the files that you would like to work on. It only supports video files, like flv, f4v, avi, wmv, mp4, mpg, mov and 3gp. It displays the file name and path on your computer.
You can convert various files to avi, mpeg2, quick time, animated gif and wmv. You can set a custom size for your video, simply adjust the options that are made available to you. Moreover, you can easily add or remove files on the list if you want.
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The application doesn’t have a built-in player, if you want to preview your files you will simply need to pick a media player installed on your computer. Other than that, it doesn’t come with any additional features like 70238732e0
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The following keywords can be used in the Keymacro configuration:
Remarks:
Conversion of a database can take a bit of time, depending on the data amount and other factors. Depending on the target environment, it might be suggested to convert only a subset of the database.
Supported Platforms:
Oracle 10g or greater, MySQL 5.0 or greater.
Available Languages:
Oracle To MySQL is available in English.
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Logarithmical induction
Prove:
$$\log_{e}n=\log_{e}k+\frac{\log_{e}(n/k)}{\log_{e}k}\log_{e}k$$
Where $n,k$ are positive integers, $k>1$.
This is what I have done so far:
$$\log_{e}n=\lim_{t\rightarrow 0}\frac{\log_{e}(1+tn)}{t}=\lim_{t\rightarrow 0}\frac{\frac{1}{n}\log_{e}(1+tn)}{\frac{1}{n}}\cdot\frac{1}{\frac{1}{n}}\cdot \lim_{t\rightarrow 0}\frac{\log_{e}(1+tn)}{t}$$
I am lost after this. Could anyone help me to prove this statement?
A:
Note that
$$\log_{e}(1+tn)=n\log_{e}(1+t/n)=n\log_{e}(1+1/n)\sim n\log_{e}(1+1/n)$$
where $f(x) \sim g(x)$ means that
$$f(x)-g(x) \xrightarrow[x \to \infty]{}0$$
For $1/n$ we have that
$$\log_{
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