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# Evaluate the limit, if it exists. $\displaystyle \lim_{x \to -1}\frac{2x^2 + 3x + 1}{x^2 - 2x - 3}$

## $\frac{1}{4}$

Limits

Derivatives

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Rr T.

February 18, 2021

Shouldn't you be using limit laws as discussed in chapter?

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

to develop it the limit of two X squared plus three X plus one over x squared minus two X minus three. As X approaches negative one know that if we directly substitute x equals negative one. We have two times negative one squared plus three times negative one plus one over have negative one squared minus two. Perhaps negative one minus three. This is equal to 0/0 which is indeterminant. And so we have to rewrite our function now. Not that we can write this into the limit as X approaches negative one of two, X plus one times expose one, this is all over x minus three times X plus one. And here we can reduce our functions since we can get rid of express one and we have limits as X approaches negative one of two, X plus one over x minus three. And so by direct substitution we have two times negative one plus one over negative one minus three. This is equal to negative one over negative four which is just 1/4. And so this is the value of our limits.

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#### Topics

Limits

Derivatives

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp