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Evaluate the limit and justify each step by indicating the appropriate Limit Law(s).

$ \displaystyle \lim_{x \to -1}(x^4 - 3x)(x^2 + 5x + 3) $

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05:46

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 3

Calculating Limits Using the Limit Laws

Limits

Derivatives

Oregon State University

Harvey Mudd College

University of Nottingham

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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Evaluate the limit and jus…

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we have a question in which we have people with the limit Limit acceptances to -1. Excellent. Really powerful minus three X and two X square plus five X. Let's see um By indicating proper limit laws and it is so let us pay attention on the law that if limit access approaching to a if we have fx and gx static product. So this can be written as limit X approaches to a fx into limit X approaches to a gxe. So let us use this. It will become Limit x approaches to -1 Exodus depart for -3 x. into limit Except for just 2 -1 at the square Plus five x plus three. No, if they use that limit X approaches to this is law will be we will use affects place G X. So this could building has a limit X approaches to a fx bless limit X approaches to a dx. So here we will be applying in both the cases this law limit X approaches to -1 x rays to depart for place Limit x approaches to -1 minus three X. Yeah limit X approaches to minus one X squared Plus limit x approaches to -15 x Plus limit x approaches to -1. Okay, okay so there is another law that if lim X approaches to a and if any function affects is multiplied with any constant term lambda. So the school Britain has limits, linda, lim X approaches to fx. It will be utilized this here. This will become limit X approaches to minus one. Access to the part four plus minus three is a constant 2 -3 limit x approaches to -1 X Limit x approaches to -1 x esquire Yes five limit X approaches to -1 x. Less limit X approaches to -1 to think it's not plugging in minus one in place of acts everywhere minus one, there's depart for plus minus three to minus one Into -1 whole square Plus five and 2 -1 Plus three because this is constant and limited constant. Is that constant? Only this is the law limit X approaches to a linda will be simply linda. Okay so this is one last three, 10 to one minus five plus three, so for into minus one That is -4 -4 should be uh answer thank you. Okay.

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