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Previous ProblemProblem ListNext Problempoint) Book Problem 1261Let f(z) Calculate lim f(x) by first finding continuous function which i5 41 equal t0 f everywhere e...

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Previous ProblemProblem ListNext Problempoint) Book Problem 1261Let f(z) Calculate lim f(x) by first finding continuous function which i5 41 equal t0 f everywhere except at = 1 (i factor and simplify)lim f(z)Preview My AnswersSubmit Answers

Previous Problem Problem List Next Problem point) Book Problem 12 61 Let f(z) Calculate lim f(x) by first finding continuous function which i5 41 equal t0 f everywhere except at = 1 (i factor and simplify) lim f(z) Preview My Answers Submit Answers



Answers

In Problems $17-38$, find the limit using the properties of limits in Theorem $2 .$ $$ \lim _{y \rightarrow-1} \sqrt{y^{2}+6} $$

Okay, so we have this limit is exposed to five of two X plus six to the one half power. Um Whenever we have a square roots here, two X plus six, the one half power is the same thing as the square root of two X plus six. What we can do as long as this is going to be positive um We can say that this is equal to the limit As X goes to five of two X plus six, then raised the one half power. So now that we have this limit, we can actually cut this up into two limits since we have the limit of two terms here that are added together. And so this is going to be equal to The limit as x goes to five two X Plus the limit as x goes to five of 6 To the 1/2 power. Um And so the limit of a constant in this case we have the limit of six is going to be equal to that constant. So this is gonna be equal to six. And what we can also do is we can take out this constant to and then multiply it by the resulting limits. So we're going to have to times to limit As X goes to five of X. And then this is just a limit of a constant. So it's equal to the constant To the 1/2 power. Um So the limit as X goes to five of X is equal to what we're going towards, which is five in this case, so this is equal to two times five plus six to the one half power, which is equal to 10 plus six, one half or 16 to the 1/2 Which is equal to plus or -4.

Hello. My name's Butler. And in this video I'm sure I'll find the limit of extra three. That's four X. Plus one. This extends to negative one. So obviously if you see a function like this and then you even drink of where it's 10. To what you simply need to do is just to plug him is value which is negative one which is constantly into the function you're given. So what we're gonna do is we're gonna play the negative one into this function. Yes. So I think this what do you have went ahead negative one To the .3. Then we have maintenance for and planning in there done here Then he weaves plus one. So evaluating this negative 123 it's negative one minus four negative one you have positive for and then minus one plus plus plus four and I have three. Then lastly three plus one he have four. So this means that the limit for functions is for. Thank you for your time.

In this problem will be using the product property of limits from Curium two to compute the given limit. So from the product property of limits, it follows that the limit as X approaches to rather negative too, of X plus three times the square root of X. Plastics is the limit. As X approaches negative two of explicit tree dime's the limit as X approaches negative. Do yeah, of the square root of X plus six. Now from here, we can just directly substitute in our values, So that's negative duplex three multiplied by the square root of negative two plus six, And we get one Times The Square Root of four, Which is just equal to two. Mhm. And that is a required limit.

All right. So we've got to find this limit or state that it doesn't exist. Um First thing we try to do is plug in um The limit. So we're going to plug in negative two for X and see if that works negative two times the root of negative two plus four. So the root of positive too. And then we've got the cube root of negative two minus six which is negative eight. That's all fine, cube rid of a negative number is fine. So we've got negative two times. Route two times. This is going to be negative too. So the limit is forward to.


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