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Find the limit.$ \displaystyle \lim_{\theta \to 0} \frac {\cos \theta - 1}{2 \theta^2} $

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00:44

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 3

Derivatives of Trigonometric Functions

Derivatives

Differentiation

Missouri State University

Baylor University

University of Michigan - Ann Arbor

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 limits.$$…

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02:46

how to solve this

02:15

it's clear. So when you read here, So we have the limit. The state approaches. Zero her co sign of data on minus one over too. Wait a square. This is equal to the limit and state approaches. Zero for co sign minus one over to beta square turns co sign plus one vulgar co sign plus one which is equal to one. You make this equal to limit a state of coaches. Ciro, we're co signed. Square minus one over too. Beta square. There's one over. CO sign street of plus one. This is equal to the limit. Data approaches zero negative. Sign square over to date. A square comes one over. CO signed data close one. We continue to simplify it. Out. We get signed. Square over. Data square runs the limit as ex approach speed approaches. Zero negative one over to post time data plus two. Then this equals the limit. Estate approaches zero for sign. They, uh, over beta square time. Negative one over to co sign of zero plus two. This equals one square turns negative. One over two plus two becomes equal to negative 14

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