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For the function $f$ whose graph is given, determine the followinglimits.$${ a. }\lim _{x \rightarrow 2} f(x) \quad \text { b. } \lim _{x \rightarrow-3^{+}} f(x)$$$${ c. }\lim _{x \rightarrow-3^{-}} f(x) \quad \text { d. } \lim _{x \rightarrow-3} f(x)$$$${ e. }\lim _{x \rightarrow 0^{+}} f(x) \quad \text { f. } \lim _{x \rightarrow 0^{-}} f(x)$$$${ g. }\lim _{x \rightarrow 0} f(x) \quad \text { h. } \lim _{x \rightarrow \infty} f(x)$$$${ i. }\lim _{x \rightarrow-\infty} f(x)$$

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02:28

Amy J.

Calculus 1 / AB

Chapter 2

Limits and Continuity

Section 6

Limits Involving Infinity; Asymptotes of Graphs

Limits

Continuous Functions

Missouri State University

Campbell University

University of Nottingham

Lectures

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in this problem for the function f who's graph is given to them in the following limits Right? So, here, for the part it is asked that limit extends to two for fx rate or you can see uh the limits for fx is exchange 22. Okay, so now here, in the graph you can see India graph you can see limit extends to limit Extends 2 to minus of ethics, right? Is equals to limit extends to two plus of effects. Right? So what does it mean? It is equal to zero? So therefore we can say we can easily imply it in this way that if left and limit is equal to the right hand limit then for sure the limit Exchange 2, 2 when we equals to zero. So this is a first answer. All right, now, moving ahead For the second question it has asked limit extends to three plus of FX is what? Right? It is as So we need to determine the limits. Alright, so here here the we can see yes, here it is. So here is some point where this is .5. Right? So this limits limit becomes for extends to three plus, it should be Nothing, but it should be .5 year. All right, now, moving ahead again, we are asked to find the limits of the function X. With limits extend to three minus. So here again it will be equals 2.5. Right, because only unique values present here at this .5 For this. Right, so this is actually .5 in the crap Okay, now for the part D we have limit Extent to -3 of fx is equal to what? So here we can see in the graph that is -3. So what is the valid value? Well it value is it? Okay -3. Where is the -3? So it should be uh this is uh this is standing to -3. Right? So here we can see here we have one value here it is -2. So the value comes out to be -2 here. Okay now for the part E. U. We can see zero plus zero plus is given to us Limit extents to zero plus of fx is what? So this is part E. So zero plus. Okay so what zero plus The limit should be, this is zero. Right? So for this there should be minus one. So the value for the zero plus extend to zero place of function X is equal to minus one year. Right? For zero minus again, proceed oh minus Right, so for zero minus it should be uh it should be Right. So for 0- We can see that here does not exist anything. Right? Right? So nothing is existing here. Yeah, so the left hand limit will be this will be infinitely. Okay this will be infinity. Right? So now here we can say for limit extents to zero of fx will be what? So for extents to zero it does not exist right Does not exist. Why? So, because left hand limit we have seen here for extends to zero plus an extent to my zero the values are different. It means that the value do not exist. You okay? All right. So now we can see here. One more thing. Okay, here, edge, for part edge we can see mm limit extends to infinity of fx is what support for infinity it will be. It will be same as infinity only. Right? And for minus infinity it will be zero. Okay, because this cuts the region right? This is cutting the region, right? So that's where 20. But this is infinity because we are getting this infinity in this form. Right? So it is not cutting the uh X axis at any point, right? At X tends to infinity. Right? But in minus infinity. Just starting to uh X axis. That means the value becomes zero. So this is how we solve this problem. I hope you understood the concept. Thank you for watching

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Harvey Mudd College

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