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Use the given graph of $ f $ to state the value of each quantity, if it exists. If it does not exist, explain why.

(a) $ \displaystyle \lim_{x\to 2^-}f(x) $ (b) $ \displaystyle \lim_{x\to 2^+}f(x) $ (c) $ \displaystyle \lim_{x\to 2}f(x) $(d) $ f(2) $(e) $ \displaystyle \lim_{x\to 4}f(x) $(f) $ f(4) $

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04:33

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Limits

Derivatives

Sanad A.

May 26, 2022

your answers are wrong for some parts that are not the same as the other video!! for same problems

Oregon State University

Harvey Mudd College

Baylor 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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in this problem, it is us that use the given graph of F to state the value of each quantity if it exists, If it does not exist, explain why. Right? So here it is given the first one limit exchange. Two to minus of fx you can say. So here the value is nearer to value of Y is nearer to, you can say here, you can see or if it will be closer to three. So the value becomes three here. Okay, so this is the answer secondly, for part B we will see limit extends to two plus efforts is given to us. That means For ex all equals greater than two only. This limit exists. Right? So that's why values three years, which is closer to, you can say do cool, X is equal to two. Now limit extends to two of fx. Fx is nothing but the value of Y at x is equal to two years assuming rate. So now this value is not defined because there are two reasons because there is an open daughters present right now. And secondly we can say limit, Extreme 2- is not equal to limit Extends to two plus for the function of X. That is why you can say now at F equals to two which is a defined value. The defined value is nothing but this is three. So this is our answer now for the party limit ethics Limit exchange to four of FX that is undefined. You can see this value is and define hi, good thing because again, there is open and open dot here. Right? So that's why this becomes a no defined values are present at X is equal as his exes equals to four years. Now. Again, f ford it is asked. Okay, so is there any value which is which is there in the defined value for airport? No, because again there is an open he looks open loop, you can say open point, you can say all, you can say the open dot, Right? So this is does not exist undeclared. Hello everyone. Yeah, So this is all you can say undefined can be written as does not exist, does not exist. So this is how we solve this problem. I hope you understood the concept. Thank you for watching.

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