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Use the graph of the function $ f $ to state the value of each limit, if it exists. If it does not exist, explain why.(a) $ \displaystyle \lim_{x \to 0^-}f(x) $ (b) $ \displaystyle \lim_{x \to 0^+}f(x) $ (c) $ \displaystyle \lim_{x \to 0}f(x) $

$ \displaystyle f(x) = \frac{x^2 + x}{\sqrt{x^3 + x^2}} $

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Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Limits

Derivatives

Campbell University

Oregon 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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Use the graph of the funct…

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Use the graphs of $f$ and …

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Mrs Problem number fourteen Stuart, eighth edition, section two point two He's the graph of the function F to state the value of each limit. If it exists, it is not explain why. So we take a look at their plot using neither crapping calculator Ah, this Excel spreadsheet or any other graphing the tool. And we take this function and plot it and we're gonna be planting around X equals zero because that is the location of interest. And to answer party the limit of this as experts zero from the left, we see that the behavior you Raph approaching through from the left is equal to negative one. And that is the left hand limit. Take a look at the graph again, per p. The limit of F as experts zero from the right. We follow the behavior of the function and we see that it approaches approximately one positive one as we traced the function from the right zero towards zero. Finally, the limit as expert is zero of the function AF has to do with both the left hand lemon and the right hand woman. They both exist, but they are not in agreement. Make it one on one are different parts of the graph and therefore we say that the limit had, as experts zero in totality does not exist.

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