Yes, it is true that the function f(n)2 is asymptotically smaller than the function g(n)2.
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It is not true that docking stations are usually smaller than port replicators. It is true that port replicators are typically smaller than docking stations. Port replicators usually do not have PCI slots or speakers.
In C programming, a precondition is a condition that must be true before a function is called, while a postcondition is a condition that is guaranteed to be true after the function has been executed.
Yes, and the general reasons are the ones you stated. They are smaller and more powerful. Main reason is because of the research it took to get them like they are.
The Nyquist theorem is a property of mathematics and has nothing to do with technology. It says that if you have a function whose Fourier spectrum does not contain any sines or cosines above f, then by sampling the function at a frequency of 2fyou capture all the information there is. Thus, the Nyquist theorem is true for all media.
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