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

## $\frac{1}{3}$

Derivatives

Differentiation

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

Hey, it's square. So when you right here. So first thing we're gonna do is we're going to factor out the denominator we get X minus one turns X plus two. We're gonna rewrite the limit as a product when we get limit as X approaches one their sign X minus one over X minus one. You're instilling as X approaches one. We're one over X plus two. We're gonna make you equal to X minus one When we get the limit, As you approach is Ciro, first sign you over you times the limit. This X approaches one. We're one over X plus two. We know that you is equal to X minus one. So the limit as X approaches, one can be be written. Asked the limit. Where were you, Ingrid? A limit. As you approach is one minus one. This becomes zero. So that's why we wrote you goes to zero. This simplifies into one. I'm limit as X approaches one of one over X plus two only. Plug in one for X. So we get one over one plus two, which gives us 1/3

#### Topics

Derivatives

Differentiation

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp