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

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00:34

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 3

Derivatives of Trigonometric Functions

Derivatives

Differentiation

Missouri State University

Harvey Mudd College

Baylor University

Boston College

Lectures

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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find the following limits …

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.

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