Limits of Rational Functions - Fractions and Square Roots
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- เผยแพร่เมื่อ 27 ม.ค. 2025
- This calculus video tutorial explains how to evaluate the limit of rational functions and fractions with square roots and radicals. It provides a basic review of what you need to do to find the limit. Whenever you a complex fraction, you should multiply it by the common denominator. If you have radicals and square roots, you should multiply by the conjugate. This video contains plenty of examples and practice problems for you to work on.
Limits - Free Formula Sheet:
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Limits - Video Lessons:
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Limits - Free Formula Sheet: bit.ly/3T3dD2X
Limits - Video Lessons: www.video-tutor.net/limits.html
Your explanation makes me want to send millions of flowers to your house to thank you 🙏🌻🌻🌻
Wth i got lost in 7:06 where does that -1 came from?
@@Josh-fg6qc It is from the equation that you modified so it can be cancelled :)
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
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
Good job
Bro. I swear I watched a hundred videos and this guy made the most sense. Gos bless him so much
This channel is the light bulb for us for calculus
You are the best online professor in the world.
Thanks!
You have no idea how you simplified math and make it fun to learn. Thank you
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
This guy is the goat man, helped me since middle school and now in college and hes still clutching up
hes so friggin helpful, i passed maths becos of his explaination holy shit THUMBS UP
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.
I've learn from him more than i've learned from my calculus teacher
This video really helps me alot in terms of using different technique.
I'm paying tuition to this guy next semester
thanks man i find it easy here than when they explain it in class.
Talented I just love really love the way you made me understand many thanks 🤗🤗🤗
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 😊
can we have a video of this topic but with x -> infinity
❤❤❤❤❤❤I love the explanation soo much really I hate math but I love the way that you send the information so thank you ❤❤
U LITERALLY SAVED MY LIFE
Thank you for this video. You've helped me so much
❤❤❤❤Thanks you are really the best
If you don't know how to get the common denominator of fractions with variiables like at 7:40, watch his other video (th-cam.com/video/MFjx52NW5Bw/w-d-xo.html)
Really your teaching is awesome
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?
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!
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)
You're a lifesaver
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
this was helpful u saved me from failing tysm
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.
can you please do a video on proving limits using the epsilon-delta definition please🙏
Bro thanks man....... It is really helpful to me
6:30 why does it have to be (-1) can't it be just (1) ? pleaaase someone answer....
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!
@@JKMath thank you🙏♥️
BRO YOU'RE THE BEST
So if the the square root was the denominator would you still multiply by the conjugate of the denominator or numerator?
You are the best😇
very clear explanation. thank you sir
very soothing voice
G 180
note:
7:33 in such case you have to multiply the function with the common denominator of the numerator .memorize it
You should do asmr bro ur voice is so soothing
really helped man! but we have this one question, what if the numerator is under only one square root
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!
I don’t get where he gets all the -1 and 1 on numerators. 😿😿
Give a timestamp
I feel pressured everytime he asked "What do you think is the answer?"
I mean sir I don't know too!😂
why in simplifying, the radical is on top but now in the denominator. I thought you cant leave a radical in the denominator??
Great content with brief explanation 10Q
please can you make a video on how to proof the limit as x approaches 2 of the the function root of x
Thanks for the tutoring
Can you solve exercise in Feliciano and uy book?
maths is really confused but thanks for your explanation
please is there a way of contacting you personally??
am grateful
How do you know when to substitute?
Thank you🙂
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
Thank you sir🥺
Question on problem at 5:02 why was the GCF -1?
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!
@@JKMath it does thanks
maayo paman kas among maestra dol oy
What if we multiply the conjugate, but when we substitute, the denominator still becomes 0? If it helps, the denominator has a radical.
Then it gotta be DNE
@@RaghedAlFarawati thanks for the response. We thought so too.
is the answer right @ 8:40?? Not 1
Wth i got lost in 7:06 where does that -1 came from?
(3 - x) = -1 (x - 3)
@@raanoooshh9296 Thanks
This is very easy it will not help me during exam of collage bc evry one can understand so give us complicated question please
Neasiir Naye do u even speak english?
Carlos Garcia Can you understand English?
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@@kobopanzon8506 XD😂😂👌
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 TH-cam
What if I had x^2 as a denominator?
^
Shouldn’t it be positive one over 3x???
Hi can you do limits at complex numbers?
what if x is only at numerator
Nice!!
Do you have an example of the second problem with a polynomial under the radical instead of a binomial?
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THANKS !!!
Can u do on upper bound and lower bound plz
Pls for the first step , can we multiply the denominator , pls someone should reply me
Like Instead of using root x+2 to multiply , can we use x+4
THX
thank you
Wth i got lost in 7:06 where does that -1 came from?
Why can I never find what I actually need help with
So good
you hELp me in ways that no one else CAN
ty so much
How about polynomials?
with double squared & cuberoot
You are beautiful. That is all I have to say right now. Wow. So helpful this is so mind-boggling
I love you man
You need to tutor mechanical science please😭
omg such a baby gurl
thanks
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.
5:13 is not a rational function
Evaluate lim √2x / x√x+7
x->3
live thank you
I love you JG
Pass Your account details Boss😂
Now I gotta go online and teach myself this bullshit cause of this coronavirus shit
He is a professor
My goat!
root(2)*root(2)= 2 , i think this is right
Was helpful tho.
Wow
Can I have your email ID sir? I have a question I was wondering you could help me with.
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you should do an episode with joe rogan