(infinity-infinity)^infinity 

Kiritsu u evil beast

Just make it the exam. Or the extra credit that gives you a huge boost.

While I have to admit it was quite tiring and time consuming, methodology wise, it was pretty simple. Not even comparable to some monster like lim( n!/n^n)^(1/n) with n approaching infinity. That’s by far the most difficult one I have ever seen

@@giannispolychronopoulos2680 yea that one is definition of hard question-simple answer.

not good not good we need more proofs related questions

I mean the exam would have to be just that question because you're using every rule in it anyway haha

Ben McKenzie This solution is unnecessary complicated, with all the fraction multiplying. Just collect x, do a MacLaurin expansion of the square roots, stopping at the first term after the 1 in order not to get 1^inf. It's going to be: lim (1 + a/x)^x = e^a, with a = -1/2, which you should know, or if you don't, you can easily find with De l'Hopital.

landochabod7 I have no idea what you’re talking about, and this is from somebody who understands everything bprp’s talking about!

I thought the same.

@@tcocaine it would be best to give this as a homework exercise.

Perhaps. In Calculus, it's customary to leave the result unrationalized.

after doing a question like that i wouldnt give a damn about rationalising the fraction lol

You mean e^1/2 ?

@@Nonexistility They just rationalized it

That's the difference between an algebra teacher and a calculus teacher.

John Dixon If you search calc2 final exam, then... :)

This is an easy one. Next up, find the limit of the needed angles to perform 3 consecutive orthographic rotations in Polar Coordinates using Quaternions while mapping it to a 3D Complex Cartesian plane where those rotations do not change its original orientation!

@@kausarmeutuwah8304 Haha! I was being a bit sarcastic! That type of problem with all of the multivariable unknowns and many partial derivatives and multiple integrations would be insane! It would probably take 3-5 whiteboards and about 30 pens and about 15 hours to do it by hand! Let's just open up Wolfram or Mathlab... let it do it for us! Get the response, can not compute!

Heavyyyyyy!!!!

Heavyyyyyy!!!!

nadia salem (I am actually a calc2 teacher loll)

blackpenredpen I just hope you don’t give this one on the finale unless it’s the only question

It's been 6 years since I took calc 2, although my teachers covered this type of limit in calc 1.

namensindüberbewertet yea I know. That's why I just circled circled loll

This is an example of the Abuse of Lopital's Rule not the use of it. Watch This Video fo learn More About the abuse of Lopital's Rule : ​ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-3vAvpeqJkEs.html​

@@pullingrabbitsouttaahat I would see it but you spelled l'Hôpital wrong

@@JakubS Thanks For Pointing Out. But I Don't Care Much Useless Things.

Or when you find out that a subset has more elements than the original set

@@seroujghazarian6343 That's not hard to do. How many integers are there in the set of values in this inclusive range of [0,1]? Simply 2. Now, how many reals are there in that same inclusive range? Infinite!

@@skilz8098 Yeah, but considering ]0,1[ has as many elements as R (cot(πx) being the bijection between them)...

@@seroujghazarian6343 Nice! I like my conjecture... Every single concept of mathematics, all branches, and levels are all embedded in the simple expression (1+1) ... Everything is derived or integrated from it. Just the act of adding 1 to itself, the application of applying the operation of addition which is a linear transformation, translation to be exact defines the unit circle. There is perfect symmetry, reflection, and a 180 degree or PI radians rotation embedded within it. It isn't directly obvious at first, but take a piece of paper and mark a point on it and draw a line segment of an arbitrary distance towards your right. Now label the starting point 0 and the ending point 1. To add 1 to this line segment or unit vector is to take the total length or its magnitude and translate it along the same line in the same direction. The tail of the new vector will be at the head of the original and the head of the new vector will be pointing at 2. By doing this the total distance is from the initial point of 0 to the new location will be 2. This turns the expression of (1+1) into the equation (1+1) = 2. This equation is actually the definition of both the Pythagorean Theorem and the Equation of the Unit Circle that is positioned at the origin (0,0). You see, we went to the right from the starting point and labeled that 1. We could of went to the left and labeled it 1 as well. However, they are opposing directions, and vectors have two parts, magnitude its length, and its sign or direction or angle of rotation. So, we can label the point to the left with -1. Here the starting point of 0 is the point of reflection, point of symmetry and the point of rotation. If we rotate the point 1 to the point -1 with respect to the initial point 0, you will make an arc that is PI radians which also takes you from 1D space into 2D space. Now we have the Y coordinates as well. This is simply due to 1+1 = 2 which is also 1x2 = 2. And this is evident because we know that a circle with a radius of one has a diameter of 2, its Circumference is 2*PI and its Area is PI units^2. We know that the Pythagorean Theorem is C^2 = A^2 + B^2. We also know that the equation of a circle centered at the origin is r^2 = x^2 + y^2... They are the same exact equation. When we look at the general equation of a line in the form of y = mx+b we know that m is the slope between two points and b is the y-intercept. The slope is m = (y2 - y1)/(x2-x1). We can let m = 1, and b = 0 and this gives us y = x. A diagonal line that goes through the origin. This line has an angle of 45 degrees or PI/4 radians above the X-axis. We know by definition that the slope is rise/run. We also see that it is (y2-y1)/(x2-x1) which is also dy/dx, change in y over change in x. If we look closer we can see that dy/dx is also sin(t)/cos(t) where (t) is the angle above the x-axis. This is also tan(t). When you look at the original equation of the line y = mx+b we can see this as f(x) = tan(t)x + b. This all comes from 1+1 = 2! Every polynomial, every geometrical shape, including vectors and matrices, their operations, even concepts in calculus such as derivatives and integrals are rooted in (1+1)! I just love how everything within mathematics is all connected and related! I'm sure you know all of these concepts but was just wanting to illustrate all of their interconnections. Yes, I take a Physical approach to mathematical induction! Why? Because without physics, or the ability to move, or translate, then the operation of addition would have no application or meaning! You can not even add 1 to itself in a scalar manner without treating them first as vector quantities. The number 1 itself is the unit vector, and the unit vector is the number 1 itself. You need physics, motion to perform the operation of addition! And as soon as you have motion, you have, limits, derivatives, and integrals!

skilz8098 very well written!

This is an example of the Abuse of Lopital's Rule not the use of it. Watch This Video fo learn More About the abuse of Lopital's Rule : ​ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-3vAvpeqJkEs.html​

@@pullingrabbitsouttaahat this link is probably an add to his content that seems controversial, probably not something to waste time one except if you wanna laugh.

Lies again? DMP Triple

: )

Crazy Drummer I am very glad too. Thank you!!!

You can do this problem with a Taylor approach, which ends up being formally written with oh notation (you need your error in the brackets to be o(1/x) to get the right final answer).

congrats on finishing calc 1

AndDiracisHisProphet hahahahahah. I like those dots on the u

that's the second time derivative.

Wats wrong with socks? I could use a few pairs. :)

It's like gifting your girlfriend with a vacuum cleaner or an iron

This is an example of the Abuse of Lopital's Rule not the use of it. Watch This Video fo learn More About the abuse of Lopital's Rule : ​ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-3vAvpeqJkEs.html​

Max Haibara tbh I think this problem would be fun but it would take me hours at least

This is the best answer

Do you mean "find a function that approaches this limit as x->inf"?

@@PixelSergey I'm not really sure.

I had that idea too, but then it quickly dawned upon me that the idea of an inverse limit is impossible. This is why:- 1) lim (2x/x) x->oo 2) lim (x²/x) x-> 2 3) lim (x) x->2 All lead to the same result, but there's no way that we can list all possible limits which lead to 2. You will say, we cannot list all the answers of ln(-1), but that's different. There's at least a system by which we can do this. We only have to keep changing the number of rotations. This case is exactly the result of 'there are different types of infinities'. You can say that ln(-1) has countably infinite answers, while the idea of inverse limit has uncountably many answers.

@@createyourownfuture3840 is it different to log1(x)? I do admit the inverse is realistically useless. My guess is if it DID have a use, it would more likely for organization (ie. Making sure that you have to raise your "answer" to e in order to fully answer the question. Maybe something with catagorization theory (I heard it's a thing, and I have no clue what it's about minus the obvious)?

This is an example of the Abuse of Lopital's Rule not the use of it. Watch This Video fo learn More About the abuse of Lopital's Rule : ​ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-3vAvpeqJkEs.html​

Itamar Rosen thanks!!!!!!

Damn, do you have a TI-89?

@@badhbhchadh most likely he didn't use a ti89, i typed it in like 2 minutes ago and it's still calculating LMAO wolfram alpha gives it in 2 seconds tho

It means that you don't trust him.

Wahyu Adi algorithm?

First order gives you 1^infinity. Second order gives you (1-1/(2x))^x

Hahahahah

Yaa its right

when solving limits where x-->inf , especially with functions that are one polynomial over another, a useful trick is to multiply both the numerator and the denominator by (1/x). keep doing this until the highest degree term is reduced to only a coefficient. then, when the limit is taken, those other terms end up being some number devided by infinity, which makes them zero. this is why he ignores all but the highest degree term; the other terms are reduced to zero.

omg.....

Omg!! I've done it. The answer is 1. I just aplied LH two times and i ended with ln(L)=0 so L is equal to 1. I take a look with geogebra and im right! I can't believe this is the first limit i've solved

OH WOW! that's impressive!!!

Could you take the limit when x goes to negative infinty and work with complex numbers? I think that would be pretty dificult (Sorry for the bad english)

@@gregorio8827 I, using my s___ty math ended up with 0, read my comment to see how I got it

ZAID SALAMEH why?

How?

scrt(e)/e still has an irrational denominator

ZAID SALAMEH "we're adults now"

jeromesnail (sqrt(e))^(-1)

Watched the video twice (and know calc) everything he does is correct I just would have done it differently

This is an example of the Abuse of Lopital's Rule not the use of it. Watch This Video fo learn More About the abuse of Lopital's Rule : ​ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-3vAvpeqJkEs.html​

Nicholas 4321 they are equivalent for large x values. more formally 2x/(sqrt(x^2+2x+3) +sqrt(x^2+3) = 2x/(x(sqrt(1+2/x + 3/x^2) + sqrt(1+3/x^2)))= 2/(sqrt(1+2/x + 3/x^2) + sqrt(1+3/x^2)) as x goes to infinity 2/x and 3/x^2 go to 0 (if this seems non-obvious, think about what happens when you divide something by a really big number, or look at their graphs) so we get 2/(sqrt(1)+sqrt(1))=2/2= 1

Nicholas Jenkins gotcha eliminating x from either the numerator or denominator seems to make it a lot easier thanks 😊

adandap yup, I like to torture myself with math! You should check out my “extreme algebra” and “100 integrals” videos : )

Doing it this way helps to see what would happen if the numbers were replaced with other numbers. lim ( sqrt(x^2 + 2x + a) - sqrt(x^2 + b) )^x = e^((a-b-1)/2) for any real a,b. The 2x needs the 2 because of the square root. Hope you make a cube root (x^3) version next >:)

This is an example of the Abuse of Lopital's Rule not the use of it. Watch This Video fo learn More About the abuse of Lopital's Rule : ​ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-3vAvpeqJkEs.html​

No because of the china flu

This is an example of the Abuse of Lopital's Rule not the use of it. Watch This Video fo learn More About the abuse of Lopital's Rule : ​ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-3vAvpeqJkEs.html​