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# Use series to evaluate the limit.$\lim_{x \to 0} \frac {1 - \cos x}{1 + x - e^x}$

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##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

Okay. You serious to evaluate the limits? All right, so we're gonna first expand cause the next and into the X and one month, one month X square over to Victoria Plasm Harold term hiring some of that square and the denominator is going to be one plus x minus one plus x plus half of that square. Of course, there's a factorial that some Harold in term of a square. Oh, which is simplified to Okay. Half of f square plus, somehow the term minus want us let you want? Yeah, Times Explorer or two. Plus some higher order terms here is actually negative. But it doesn't matter, though, which is 91.

University of Illinois at Urbana-Champaign

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Series

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp