Graphic way of organizing concepts proposed during brainstorming. Co-op Co-op Cooperative learning method where teams work to prepare and present a topic to the whole class. Emphasis is on student selection of topics, partners, division of labor, methods of presentation, etc. Coaching Model A model of instruction where the teacher is a guide and collaborator in the student's learning, not the sole director.

A Reanalysis of Eichstaedt et al. In our original article, we showed that Twitter language, fed into standard machine learning algorithms, was able to predict i.

Further, in a separate analysis, we found that the dictionaries and topics i. Beyond conducting a new analysis correlating Twitter language with suicide ratesBrown and Coyne also detail a number of methodological limitations of group-level and social media-based studies. We discussed most of these limitations in our original article, but welcome this opportunity to emphasize some of the key aspects and qualifiers of our findings, considering each of their critiques and how they relate to our findings.

Of particular note, even though we discuss our findings in the context of what is known about the etiology of heart disease at the individual level, we reiterate here a point made in our original paper: Our findings are intended to provide a new epidemiological tool to take advantage of large amounts of public data, and to complement, not replace, definitive health data collected through other means.

We offer preliminary comments on the suicide language correlations: Previous studies have suggested that county-level suicides are relatively strongly associated with living in rural areas Hirsch et al.

When we control for these two confounds, we find the dictionary associations reported by Brown and Coyne are no longer significant. We conclude that their analysis is largely unrelated to our study and does not invalidate the findings of our original paper. In addition, we offer a replication of our original findings across more years, with a larger Twitter data set.

We find that a Twitter language still predicts county atherosclerotic heart disease mortality with the same accuracy, and b the specific dictionary correlations we reported are largely unchanged on the new data set.

To facilitate the reproduction by other researchers of our original work, we also re-release the data and code with which to reproduce our original findings, making it more user-friendly. We will do the same for this replication upon publication. Diachronic degradation of language models: Insights from social media Jaidka, K.

Insights from social media.To find a power series for the function, centered at 0. f(x) = 18 (x + 1)3 - Write the Maclaurin series for arctan(x2). Write the Maclaurin series for an antiderivative of arctan(x2).

Use the binomial series to expand the function as a power series. 7 (6 + x)3?

Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more than once). In Note \(\PageIndex{1}\), we state results regarding addition or subtraction of power series, composition of a power series, and multiplication of a power series by a power of the variable.

For simplicity, we state the theorem for power series centered at \(x=0\). The Power Series Representation of an Entire Function.

Now we have Cauchy’s Theorem, we are now able to prove the major ﬁrst result we shall see in complex analysis - the fact that any entire complex function can be represented as a power series. Theorem (Taylor Expansion of an Entire Function) Suppose that f(z) is an entire function.

Added Nov 4, by sceadwe in Mathematics. A calculator for finding the expansion and form of the Taylor Series of a given function. To find the Maclaurin Series simply set your Point to zero (0). Several important formulas, sometimes called logarithmic identities or logarithmic laws, relate logarithms to one another..

Product, quotient, power, and root. The logarithm of a product is the sum of the logarithms of the numbers being multiplied; the logarithm .

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Properties of Power Series - Mathematics LibreTexts