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# Find the Maclaurin series of $f$ (by any method) and its radius of convergence. Graph $f$ and its first few Taylor polynomials on the same screen. What do you notice about the relationship between these polynomials and $f?$$f(x) = \cos (x^2)$

## $\sum_{n=0}^{\infty}(-1)^{n} \frac{x^{4 n}}{(2 n) !}, \quad R=\infty$

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##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Samuel H.

University of Nottingham

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### Video Transcript

the problem is finding Michael Oren. Siri's off off on this really is burdens Graff half on DH. It's rest of futile Oprah Nahmias on the same screen. What do you notice about a relationship in this half? Half of axe is equal to assign X koi supposed to have signed X if they caught you some from zero to infinity If you want to end times X to Teo over to end Vittorio then we replace acts by ex Squires We've got a flex. This is Nico saw from zero to twenty. Next you want and hams Axe too foreign over to end. I love you. There were computers, a radius of convergence Damn it and crossed the infinity. Absolutely. Oh, ax to four end or over to him Last two factorial times. Yeah, two in fact, Arial over tax to foreign. This is a limit cost Trinity I just for over two possible one halves to, uh, pass too, which is equal to zero. The readers of convergence is going to be fine. That's little cat. It's graphs. Zariah curve is have a lax green one. This is zero. The blue one. This she wants on our angel Juan is too notice that, as in increases, he index becomes a biting approximation to the function Kasai X Square.

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#### Topics

Sequences

Series

##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp