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

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$\frac{1}{3}$

01:21

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 3

Derivatives of Trigonometric Functions

Derivatives

Differentiation

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04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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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

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