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

$ \displaystyle \lim_{x \to 3}(5x^3 - 3x^2 + x - 6) $

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105

04:54

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 3

Calculating Limits Using the Limit Laws

Limits

Derivatives

Oregon State University

University of Michigan - Ann Arbor

University of Nottingham

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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And we have a question in this military. Well with the limit and by using step by step method and including law laws which are being used, Question is limited approaches to three by xq minus three action Squire less X minus six. So we'll be using a lot of that if lim X approaches to a fx plus G X. Like this. So this could Britain has limited distributed basically X approaches to a affects place limit X. A process to a dx. So from here it will be Yeah limit. Okay Limit x approaches to three five X skills bless limit X approaches to three -3. x esquire bless Limit x approaches to three X. Place limit X approaches do three -6. Okay, now we have another law that if this is constant so this can be taken out as limit X approaches to a Uh huh. Let us say linda. Fx. Well linda is any constant so this can Britain has lambda limit X approaches to a ethics Okay, No, this is five limit X approaches to three x cubed plus minus three limit X approaches to three X squared bless limit X approaches to three x minus a place minus six Limit except three. So this will be simply -6. Okay, so this is we will be plugging in here you bless minus three. Three square bless three bless minus six. 135 minus 27 Plus 3 -6. Yeah, So this is my 33 minus 30. 105 for 105. Should be dancing. Thank you

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