Limits of Rational Functions - Fractions and Square Roots

[@TheOrganicChemistryTutor]

Limits - Free Formula Sheet: bit.ly/3T3dD2X Limits - Video Lessons: www.video-tutor.net/limits.html

[@SABA-og3jv]

Your explanation makes me want to send millions of flowers to your house to thank you 🙏🌻🌻🌻

[@Josh-fg6qc]

Wth i got lost in 7:06 where does that -1 came from?

[@atp4223]

@@Josh-fg6qc It is from the equation that you modified so it can be cancelled :)

[@LaninaMelissa]

I took a break after finishing community college and am now in university taking my first calculus course in years. You are saving my life, sending a million kisses and presents to you

[@jhaillarrymaegarcia131]

Thank you for posting this. This is the one that I really need right now. My teacher didn't show us on how to solve these. You literally makes my life easier. Gonna share this to my friends and siblings who's now a STEM student too

[@smileydeception1947]

Once again, Thank you! You've really helped me learn a LOT more than any other teacher in my life. I can't thank you enough. You're a blessing to people who have a hard time in Math. God bless you more!! :3

[@Ajalgai]

Good job

[@Magnetshroom]

This channel is the light bulb for us for calculus

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[@tongmuli3747]

You are the best online professor in the world.

[@mahaabdullahalghamdi686]

You have no idea how you simplified math and make it fun to learn. Thank you

[@emmanuelgreen8553]

Thanks!

[@georgesadler7830]

MR. Organic Chemistry Tutor, thank you for explaining Limits of Rational Functions in Calculus. The first example can be factored. X - 4 can be factored into the square root of x minus 2 times square root of x plus 2 on the denominator. By cancelling square root of x minus 2 on the numerator and denominator yields the same solution in the video.

[@moorpatton]

Thank you! You've really helped me learn a LOT more than any other teacher in my life. I can't thank you enough. You're a blessing to people who have a hard time in Math. God bless you more!! :3

[@sebastianmartin8736]

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[@mzaddiction23]

Thank you so much. Your videos are so helpful. I taking this class online and it’s overwhelming. So this gives me an idea of how to approach the problem 😊

[@julietpershia5788]

I've learn from him more than i've learned from my calculus teacher

[@RaghedAlFarawati]

I'm paying tuition to this guy next semester

[@mathewsilu]

This video really helps me alot in terms of using different technique.

[@chikkys.m.1593]

can we have a video of this topic but with x -> infinity

[@rosenyakhortuong7993]

Talented I just love really love the way you made me understand many thanks 🤗🤗🤗

[@sinicized8344]

For the example at 0:44 you could factor the bottom to sqrt x + 2 and sqrt x - 2 cancel and get 1/sqrt x + 2 ( the same answer)

[@existential_narwal9257]

thanks man i find it easy here than when they explain it in class.

[@Do_Go0d]

Thank you for this video. You've helped me so much

[@MiraHanafy]

U LITERALLY SAVED MY LIFE

[@kassiebattle8279]

What would you do if you had a problem similar to these, but the limit is exclusively approaching from just the left or just the right?

[@JKMath]

In most cases, the limit from one side would be fairly similar to taking the derivative of these functions from both sides. If you can plug in the value of x that you are approaching without coming across 0 in the denominator, you are good to go. However, if you come across a problem where plugging in the value results in 0 in the denominator, you have a few different options. One option would be to try and simplify the function, using the techniques shown in this video until you are able to plug in the value without getting 0 in the denominator (so nothing different from a two-sided limit as shown in this video). And a second option would be to plug in values close to the value of x that you are approaching from the appropriate side. This comes in handy when there is no way to reduce your function, such as a function like 1/x as x approaches 0. So for example, if you had the limit of 1/x from the right, you plug in positive values closer and closer to 0 such as 0.1, then 0.01, then 0.001, and so on, and see what your output is getting closer to (in this case it would be getting closer to positive infinity). And then from the left side you would plug in values less than 0, or negative values, such as -0.1, -0.01, -0.001, and so on and look at where those output values are heading (negative infinity in this case). Hope this helps!

[@erazn9077]

I was confused on when i should foil/multiply the stuff underneath the fraction, but i realised that when the denominator has problem areas, like a variable that can equal 0, we need to get rid of that variable, and multiplying it by the other term isn’t gonna help. The point is to cancel it out.

[@surajjani4868]

Really your teaching is awesome

[@ladislousfarawadya5115]

can you please do a video on proving limits using the epsilon-delta definition please🙏

[@Samar-h9g]

❤❤❤❤❤❤I love the explanation soo much really I hate math but I love the way that you send the information so thank you ❤❤

[@samiulislamdurjoy]

G 180 note: 7:33 in such case you have to multiply the function with the common denominator of the numerator .memorize it

[@injusticegods_yt2617]

I understand but the only issue is I forgot how the multiplication works when you do the stuff I get confused please show work how you multiply the radicals and stuff

[@1nfuzion]

If you don't know how to get the common denominator of fractions with variiables like at 7:40, watch his other video (kzbin.info/www/bejne/g3fNqWhog7xoeNk)

[@xS0G0N3x]

You're a lifesaver

[@estherobot7619]

this was helpful u saved me from failing tysm

[@FrankKanyembo-x4u]

So if the the square root was the denominator would you still multiply by the conjugate of the denominator or numerator?

[@chethanmalik7641]

Bro thanks man....... It is really helpful to me

[@psychoticblackmakeup]

very soothing voice

[@jjjjjjjjjj00]

6:30 why does it have to be (-1) can't it be just (1) ? pleaaase someone answer....

[@JKMath]

Since there was a quantity of (x-3) in the denominator, and he waned to try and reduce the function by factoring that out, it was in the best interest to try and manipulate the 3-x on the top. Factoring out -1 negates that quantity and allows it to become -3+x which can then be re-arranged to be x-3, which can then be factored out from the function entirely since that quantity is also in the denominator. It was not positive 1 because factoring out positive 1 does nothing to a function since anything multiplied or divided by 1 is just itself. You can always factor out -1 from a function, as it just negates each value in the quantity you are factoring it out of. For example, x+5 would be equal to -1*(-x-5) if you factored out -1. Another example would be factoring out -1 from (-4-x) to get -1*(4+x). Just don't forget to keep that -1 after you do your cancelling out/factoring! Hope this helps!

[@jjjjjjjjjj00]

@@JKMath thank you🙏♥️

[@fhulufhelonengome4542]

You are the best😇

[@apsietese8718]

very clear explanation. thank you sir

[@raphaelrevilla1873]

really helped man! but we have this one question, what if the numerator is under only one square root

[@JKMath]

Do you have a particular example you are stuck on? If the numerator is all under one square root, the solving technique really depends on what is in the denominator. If you can just plug in the value of x you are approaching into the function without getting 0 in the denominator, you should be able to find the limit that way. If you still need help let me know, I'd be glad to help!

[@Samar-h9g]

❤❤❤❤Thanks you are really the best

[@pinkkk]

BRO YOU'RE THE BEST

[@Circa1628]

why in simplifying, the radical is on top but now in the denominator. I thought you cant leave a radical in the denominator??

[@tdukeluke260]

It doesn’t make sense that x-4 substitutes to 1 if the limit of x is 4. Shouldn’t it be 0? Edit: I’m dumb the values cancel

[@wahaabmujtaba5250]

You should do asmr bro ur voice is so soothing

[@masterjohnpax6294]

I feel pressured everytime he asked "What do you think is the answer?" I mean sir I don't know too!😂

[@kazuosenpaiph9254]

Can you solve exercise in Feliciano and uy book?

[@zodiiiocdenaria2638]

maayo paman kas among maestra dol oy

[@kageyamatobio-h4q]

please can you make a video on how to proof the limit as x approaches 2 of the the function root of x

[@gudapodcast]

Great content with brief explanation 10Q

[@neasiirnaye9121]

This is very easy it will not help me during exam of collage bc evry one can understand so give us complicated question please

[@kobopanzon8506]

Neasiir Naye do u even speak english?

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Carlos Garcia Can you understand English?

[@kobopanzon8506]

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[@fatemanessa5124]

@@kobopanzon8506 XD😂😂👌

[@fatemanessa5124]

Smartass spotted. This is for basics only. Not a lot of people are privileged as you are that they will have great access to materials like these. Be glad it's out there helping hundreds of thousands understand what these things are. Some cant even start the chapter because they lack the fundamentals. Read a book if you want complex shit instead of watching stuff on KZbin

[@yowwhihi6073]

What if we multiply the conjugate, but when we substitute, the denominator still becomes 0? If it helps, the denominator has a radical.

[@RaghedAlFarawati]

Then it gotta be DNE

[@yowwhihi6073]

@@RaghedAlFarawati thanks for the response. We thought so too.

[@malatiahsakyi7745]

am grateful

[@wilyz360]

Thanks for the tutoring

[@logicnext9230]

Thank you sir🥺

[@reyn77_u]

I don’t get where he gets all the -1 and 1 on numerators. 😿😿

[@Kepplar]

Give a timestamp

[@casualiscasual]

Question on problem at 5:02 why was the GCF -1?

[@JKMath]

Since there was a quantity of (x-3) in the denominator, and we want to try and reduce the function by factoring that out, it was in the best interest to try and manipulate the 3-x on the top. Factoring out -1 allows this quantity to become -3+x which can then be re-arranged to be x-3, which can then be factored out from the function entirely since that quantity is also in the denominator. You can always factor out -1 from a function, as it just negates each value in the quantity you are factoring it out of. For example, x+5 would be equal to -1*(-x-5) if you factored out -1. Another example would be factoring out -1 from (-4-x) to get -1*(4+x). Just don't forget to keep that -1 after you do your cancelling out/factoring! Hope this helps!

[@casualiscasual]

@@JKMath it does thanks

[@blueastro4722]

Thank you🙂

[@anotherguy5038]

Lay not up for yourselves treasures upon earth, where moth and rust doth corrupt, and where thieves break through and steal: But lay up for yourselves treasures in heaven, where neither moth nor rust doth corrupt, and where thieves do not break through nor steal: For where your treasure is, there will your heart be also. Matthew 6:19-21

[@vinkelast9750]

How do you know when to substitute?

[@Josh-fg6qc]

Wth i got lost in 7:06 where does that -1 came from?

[@raanoooshh9296]

(3 - x) = -1 (x - 3)

[@supahx1421]

@@raanoooshh9296 Thanks

[@kiseananewman4220]

What if I had x^2 as a denominator?

[@bean_sproout]

^

[@OliveHappi]

Nice!!

[@zubair1424]

is the answer right @ 8:40?? Not 1

[@pinedama.isabelles.8380]

Hi can you do limits at complex numbers?

[@richardadamwais9734]

maths is really confused but thanks for your explanation

[@pyroboi5291]

Shouldn’t it be positive one over 3x???

[@Nononsensetv]

please is there a way of contacting you personally??

[@elizabethelias1679]

Can u do on upper bound and lower bound plz

[@princessdapito8375]

what if x is only at numerator

[@shogologz6097]

omg such a baby gurl

[@Plarux]

Do you have an example of the second problem with a polynomial under the radical instead of a binomial?

[@factified9892]

Correction: In the first part, we can actually write x - 4 = (root x)^2 - (root 4)^2, then we get (root x) - 2 in the denominator which cancels the one in the numerator and we get an answer to the question.

[@dropd1695]

ty so much

[@kazuosenpaiph9254]

How about polynomials?

[@kazuosenpaiph9254]

with double squared & cuberoot

[@thoeunjoker6178]

So good

[@gantherporras4689]

Evaluate lim √2x / x√x+7 x->3

[@ahamedmotunrayo4705]

Pls for the first step , can we multiply the denominator , pls someone should reply me

[@ahamedmotunrayo4705]

Like Instead of using root x+2 to multiply , can we use x+4

[@amelgrb7965]

THANKS !!!

[@honey-marie1496]

You are beautiful. That is all I have to say right now. Wow. So helpful this is so mind-boggling

[@simbarashesithole5454]

thank you

[@Josh-fg6qc]

Wth i got lost in 7:06 where does that -1 came from?

[@noornaqvi8625]

you hELp me in ways that no one else CAN

[@aminaattar833]

thanks

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I love you man

[@bernhardhhh1143]

THX

[@chuyvazquez393]

Why can I never find what I actually need help with

[@faith4365]

You need to tutor mechanical science please😭

[@moonakam7029]

live thank you

[@yanggang4352]

5:13 is not a rational function

[@WICKLIFFMUMBA]

He is a professor

[@jaelonsanders5878]

Now I gotta go online and teach myself this bullshit cause of this coronavirus shit

[@mayurii_]

Was helpful tho.

[@AmazingDerick]

Pass Your account details Boss😂

[@DannyOvox3]

I love you JG

[@sahadat.hossain1]

root(2)*root(2)= 2 , i think this is right

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Wow

[@patarcher9199]

My goat!

[@mayurii_]

Can I have your email ID sir? I have a question I was wondering you could help me with.

[@JJWAD]

just use l'hospital's rule for all of these lmao

[@captrien]

Lol ya but when you're being tested before they even teach you l'hopital, you cant really just use it

[@JJWAD]

@@captrien yeah, i was just reviewing these vids for the ap calc exam and i saw you could just use lhospitals rule. but of course if you havent learned derivatives you cant do limits by lhospitals rule.

[@captrien]

Oh good luck on ur exam. I took AP calc too but didnt do the exam so Im here studying for midterm for this Calc 1 course and teacher havent got to l'hopital yet lol

[@JJWAD]

@@captrien Good luck too. I had the AP exam last week and it wasn't too bad. Btw, he has a great vid on l hospital's rule that i used: kzbin.info/www/bejne/qpmon5-VnKidjqM. This channel is literally my life savior lol

[@Josh-fg6qc]

Wth i got lost in 7:06 where does that -1 came from?