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Compute the indicated limit.$$\lim _{x \rightarrow \infty} \frac{(4 x-3)^{2}(x-1)}{(2 x-1)(x+1)^{2}}$$

$$8$$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 4

Limits at Infinity, Infinite Limits and Asymptotes

Derivatives

Missouri State University

Campbell University

Oregon State University

Harvey Mudd 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.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

00:58

Find the limit.$$\…

02:03

Find limit

Hello. We have to find the limit. Extends to animated limit extends to infinity. What else? Minus three. Older. Square multiplied X one is one and upon two weeks. My husband who as much as you like experts express month cool is cool. We can limit extension PD. Yeah, limit. We have to solve this limit. Yeah. Okay, so limit accidents when P t v evil. Okay, X comin from this and this also. So it will be X square four minus three y x, and we will take X comin from this. So it will be expand management by X. Yeah. So see import dysfunction. And this so x two management by X multiplied by X squared one plus one by X holy square. Right? No X squared equals square An x from X and so loud and it will be limit exchange two in 24 minus three Y x one minus one by x upon to minus one by eggs one plus one by X Holy square. Yeah. Okay. Yeah. Mhm. So now we will put the limit. It will be four minus zero. Multiplied by one minus zero upon to minus zero. It will go the script and 10 political will be 16. About two will be eight. I hope I answered revolution. Thank you.

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