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The notation lim f(x) means t0 find the limit as approaches from the left only, and lim f(x) means t0 find the limit as x approaches from the right only: These are ...

Question

The notation lim f(x) means t0 find the limit as approaches from the left only, and lim f(x) means t0 find the limit as x approaches from the right only: These are X-a X-a called one-sided limits . Find lim 2xv64 - x2 X-82xv64 - x2 X-8

The notation lim f(x) means t0 find the limit as approaches from the left only, and lim f(x) means t0 find the limit as x approaches from the right only: These are X-a X-a called one-sided limits . Find lim 2xv64 - x2 X-8 2xv64 - x2 X-8



Answers

$\lim _{x \rightarrow a^{-}} f(x)$ means to find the limit as $x$ approaches a from the left only, and $\lim _{x \rightarrow a^{+}} f(x)$ means to find the limit as $x$ approaches a from the right only. These are called one-sided limits. Solve the following problems. $$\text { For } f(x)=\frac{x}{|x|}$$,$$\text { find } \lim _{x \rightarrow 0^{-}} f(x) \text { and } \lim _{x \rightarrow 0^{+}} f(x)$$.Is $f(x)$ continuous at $x=0 ?$ Explain.

Hello franks. We have to find the limit exchange two minus of fx. This is the one sided limit limit Extends 2 to- of FX. Okay, so when actually approaches to the to from the left, the value of the function is about to zero. Okay so this is zero. This is a party. And for the part we we have to find the limit Exchange two Plus of FX. Okay, So when I exit the approaches to the zero From the right the value of function is about 20 and we have to find the limit exchange or two of effects part C Limit extension two of FX. We know that this is the NHL and this is the origin and naturally cost to origin. That is because too zero. So the limit value is also zero. So these are the final answer. I hope. You're not sure. Thank you.

Hello friends. We have to explain why LTD exchange 20 plus to the power of And my ex is not request to Limit Exchange 20 To the power off one way x. Not because to well well we have to explain this and we know that this is that I can limit. This is the last time limit. So first we will calculate that a right hand limit. Okay, so limit Extent to zero plus to the power of one by X. No, we will All right we will substitute X. He calls to zero plus edge And the edge tends to zero. So this will be caused Limit. Edge turns to zero to the power of we went up on edge when before the value then this will be a cost to invented that is in Freddie. Okay. And the left hand limit Now we'll solve the Latin level limit. Experience with 0 0 to the power of one by X. So we will substitute exit close to zero minus of edge and Edge is very small community that is extends to zero. So we can decide limit. Edge turns to 0 to the power of -1 upon it. Now we will put the limit so it will be cause to minus of. I invented that. Mhm. Baby cost zero. So a little is not because to origin. So that's why limit extends to zero. That's to the power of one by X. Is an arctic custard limit extends to zero minus off to the power of one of my ex. I hope your national. Thank you.

Hello. We have to find the limit. We have to solve the following problems. Is there a difference between the limit Extends for two months When upon X -2 and the limit extension two plus one of one. X minus. Cool. Okay so we will sub suit at the cost to minus H and at its very small countries where Justin structural limit At returns to zero. Uh huh spill for the limit So 2 -40 -2. So it will be cost too mine. When now we will put the limit so it will be cost to minus been upon jurors with minus of and beauty. So here we will substitute X by two Plus S and urges very small quantity. So we will find the limit I had to turn ST zero went upon two plus edge minus of two. So now we will for the limits that will be in 30. So is there any difference? Yes there is a difference between the limit, Yes there is between the yes there is a difference. So the value of the limit exchange too, 2- of FX. That is when upon X -2 is minus awfully pretty. And the limit extends to two plus one. Upon Ex Minister will be cause to infantry. So this is there answer? I hope you understood. Thank you.

We want to skips a graph of a function that has all of these properties for limits. So just go ahead and start with the 1st 1 So it says as extra purchase two. We wanted to go too negative Infinity. So that means it's gonna come from each side. So let's go ahead and put two domes so here would be to and then they want They've got a class into approaching negative infinity like this. So we got that one. The limit as we approach zero from the right needs to be infinity. That means over here should be going towards infinity. So we got that one. It says to the left of zero, we want to go too. Negative infinity. So over here we got a negative infinity. Then it says that as X goes to infinity fx ago to positive Pittoni. So that means we just kind of have a go out like that. And then lastly, it says that as X goes the negative entity, we should go to zero. So something kind of like this. So we got all of these time Now let's just go ahead to connect our lines so we would need to connect these two like this. Then we will need to connect these two and then the last one over here. And let's just go through to make sure that we have everything we need. So as extra purchase to it goes to negative infinity. So that one still good as it approaches here from the right stupid deposit affinity. They're from the left. Negative affinity X goes to infinity. It goes off to infinity as well. And then on the left, as exclusive negative parent function goes to zero. So this is just one possible sketch, uh, a function with these limits.


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