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Find the limit, if it exists. If the limit does not exist, explain why.

$ \displaystyle \lim_{x \to 3}\left( 2x + | x - 3 | \right) $

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01:37

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 3

Calculating Limits Using the Limit Laws

Limits

Derivatives

Campbell University

Oregon State 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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Find the limit, if it exis…

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to evaluate this limit, note that The absolute value of X -3 has two values. The first one will be Negative of X -3 If X -3 is less than zero Or that access to less than three And it will be a positive X -3. If X -3 is greater than zero or That X is greater than three. And so to find this limit, you have to do the one sided limits first. That means we do limit as X approaches three from the left of two, X plus. In this case we will use Negative of X -3. Since you're looking at Left values of three and evaluating we will get two times three minus we have three minus three. This gives us a six and the limit As X approaches three from the right, We will then use X -3 for the absolute value and so we have two X plus x minus three and this will give us two times three Plus 3 -3 Which is also equal to six. Now, since the one sided limits are equal, let me say that the Limit as X approaches three of to express the absolute value of X -3 exists and it is equal to six. That means we have limits As X approaches three of two, X plus Absolute value of X -3, this is equal to six

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