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# Find the limit.$\displaystyle \lim_{x \to 0} \frac {\sin (x - 1)}{x^2 + x - 2}$

## $$\lim _{x \rightarrow 0} \frac{\sin \left(x^{2}\right)}{x}=0$$

Derivatives

Differentiation

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##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

Yes, they're still in Yuma right here. So we have the limit. This X approaches. Zero first sign of X. Where over EPPS. You multiply the top and bottom by at this. Gives us the limit. That's X approaches. Cereal for sign of X square over X Square terms X over one, which is equal to the limit as UPS approaches. Zero. Your sign of exploring over X square turns the limit. That's that's a purchase cereal for we're gonna substitute X square data into this part. We get limit. That's data Roaches. Zero were signed data over beta times the limit. X approaches zero. You know that this is one. This is zero. We'll find them together, you get through.

#### Topics

Derivatives

Differentiation

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp