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# Use the definition of a Taylor series to find the first four nonzero terms of the series for $f(x)$ centered at the given value of $a.$$f(x) = \ln x,$ $a = 1$

## $f(x)=(x-1)-\frac{1}{2}(x-1)^{2}+\frac{1}{3}(x-1)^{3}-\frac{1}{4}(x-1)^{4}$

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##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

The problem is, use the definition of Attila Siri's to find a first born and zero terms off the Siri's. For relax. Centered is a given volume off. Hey, so first you have one day, see what zero I've X from. Say what? One over max. So half problem on one issue. One second derivative secret Addictive one over X squire. So have crumb crumb at point one zero two to one. Asked crime from prom as they called you to our backs. Q. So, prom, prom, prom one acts because it's a good one. This is equal to true in the first four Nancy with terms of Siri's. Relax when also need Thio Compute most decorative, cystic or too active truth towns. Three. Over Act two. Four. So a fruit fourth directive is appoint one. It's called connecting six. Then the first born and zero terms of the Siri's or relax centered cut one. Dennis precipitously one over one times X. Second, this is ninety one over to factorial exclaim his X minus one next month. One squire, us two over should have three x minus Wass Cube. Ask ninety six over two times three counts for excellence. One to the public for so this's equal to X minus one US LINUS one over two x minus one Squire plus one over three X months one cube minus one War X minus one through four This other first two four nine zero terms.

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##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp