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Each limit represents the derivative of some function $ f $ at some number $ a $. State such an $ f $ and $ a $ in each case.

$ \displaystyle \lim_{\theta \to \pi/6} \frac{\sin \theta - \frac{1}{2}}{\theta - \pi/6} $

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01:38

Daniel Jaimes

01:03

Tyler Moulton

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 7

Derivatives and Rates of Change

Limits

Derivatives

Baylor University

Idaho State University

Boston College

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

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.

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Each limit represents a de…

Let's talk about this question. We are given a limit and this limit actually represents the derivative of some function f. At some number eight. Uh So if you remember the derivative is nothing but the slope. So if this is the co and this is one of the point A comma F. And this is another point B comma F B. Then it's derivative is nothing. But the slope which is F B minus F or b minus A. But if a approaches to be a approaches to be or in other words, a N B overlap. So that becomes a tangent. And then we represented as a limit uh is approaching towards B is approaching towards B uh F B minus F or b minus. So that's the required derivative. So if you compare it but does limit. So we are we are given that the function is scientific because data is now approaching two priority. So we're going to say that the function there's nothing but the scientist and the value of A is nothing but uh F B minus F. So F. A. When we're gonna port which value of tita is such that when we put over here we get 1/2. So that's clearly pi over six. Because if you put by over six signs by over six is one or two or scientific degrees one or two. So the value of A. Which we are going to use this by over six. So this actually represents the derivative of the function scientific to at equal to five or six. Thank you

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