How to prove a function is infinitely differentiable? Let s(x) and c(x) be two functions satisfying s' (x) = c (x) and c' (x) = -s (x) for all x. If s (0) = 0 and c (0) = 1, prove that (s(x))^2 + (c(x))^2 = 1. ...
There's also a common trap where "significant" is used interchangeably with "important." While this might work in everyday conversation, in the realm of statistics, "significant" has a very specific meaning - it refers to the likelihood that a result is not due to random chance. That said...
Once you’ve found something you’re excessively interested in, the next step is to learn enough about it to get you to one of the frontiers of knowledge. Knowledge expands fractally, and from a distance its edges look smooth, but once you learn enough to get close to one, they turn o...
So, you've done it — you've found the role you want to apply for. Finding that perfect position where the job description matches your resume to a T is an exciting experience. Now you need to make sure your application gets you that interview. That's why you need to learn how to ...
How and to what extent can we preserve (or even increase) the value of forests? Our analysis addresses the value of forests across four attributes: their climate regulatory function; their environmental benefits, such as air purification and water filtration; their commercial output; and their ...
Specifically, the extent of credit-related losses is a function of how far house prices are above long-term trend and the extent to which they can fall below trend. Focusing on the latter, we develop a theoretically-based statistical technique to identify a conservative lower bound (CLB) for...
Economy”—have begun rethinking the relationship between law, economy, and politics suggested by the Twentieth-Century Synthesis.Our ambitious hope is to replace the current “common sense” of legal scholarship with a new set of default ideas that will prove more responsive to the crises that ...
Enter the "vaccine passport." In this brief primer we'll help you understand just what is a vaccine passport, how does it function, and where can you expect to need it. This is our explainer on the rise of the COVID-19 vaccine passport. ...
directions to function properly. Therefore, it is not attached very tightly at the tip or top of the tongue. If the back of the tongue is large or if the tongue can slip backward, it can narrow the space through which air flows in the pharynx, which can lead to vibrations and snoring...
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