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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) = \ln (1 + x^2)$

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

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##### Top Calculus 2 / BC Educators   ##### Samuel H.

University of Nottingham Lectures

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### Video Transcript

the problem is finding the McLaren. Siri's half Andi It's radius of religions Graph on its first of beauty Nahmias. Same screen. What do you notice about the relationship between this phenomenal A flood after relax is go to hell in one aspects. Coy. First two behalf on one class acts this They could sum from one to twenty. Thank you. Want the public to minus one hands. Thanks to end over here, then we replace X X square. So we're half after Lex. It's going to help. Long past Exploiter, This is a good song. Want to serenity make you want to The Tower of London Town Sacks to to end Over here there were computers, a radius of emergence Lim and cost Trinity. I have swallowed off. Next. You want extra to have us too. Over Plus one arms and hope for max to two. House nine one one. Which is here too. I scored like this. That's a once over. The readers of convergence is equal to one the original cast and that's it. This graph of the last box divider one is, uh, screw off. How? In one plus x square black wind This one two blue want misty to That's a green one sixty three. We can see that as any increases he and Max becomes, um, fight approximation to the function how in one plus X Y.

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##### Top Calculus 2 / BC Educators   ##### Samuel H.

University of Nottingham Lectures

Join Bootcamp