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Explain what it means to say that$ \displaystyle \lim_{x\to1^-}f(x) = 3 $ and $ \displaystyle \lim_{x\to1^+}f(x) = 7 $
In this situation is it possible that $ \displaystyle \lim_{x\to1}f(x) $ exists?Explain.
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03:54
Daniel Jaimes
Calculus 1 / AB
Chapter 2
Limits and Derivatives
Section 2
The Limit of a Function
Limits
Derivatives
Missouri State University
Campbell University
Idaho State University
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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So here we have a graph. And let's say that the limit As extra approaches one from the left as a five X is equal to three, that would look something like this. Our function as it approaches Our X Coordinate one. Our white corner is approaching three. All right now, let's say we also had a limit As X approaches one from the right. And that is what our plus sign here means here are negative means from the left. Plus is from the right Is F of X is equal to seven. Balance. Say I would look like something let's say like this. So here our function as we approach from the right side as we are approaching one on the X coordinate, Our function is approaching seven on the Y coordinate from the left. It's as we're approaching one on the X cornets approaching three. So as our limit is approaching one from the left, it's not equal to our limit As X approaches one from the right, meaning that there is no limit at X equals one.
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