Top 4 Algebraic Tricks for Computing Limits
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- Опубликовано: 6 окт 2024
- We look at four common algebraic tricks used to compute limits, and see four examples of them. In all cases, these tricks help to take a limit which is in an indeterminant form (ex 0/0) and convert it into a determinant form that you can compute.
Factoring: Separating out the same factor from the top and bottom means you can cancel it
Expanding: Sometimes you need to multiply out and expression before you can see the canceling
Common Denominator: When you have a sum or difference of fractions, you can combine the fractions into a single one with a common denominator
Radical Conjugate: When you have expressions with square roots, often the radical conjugate is the trick you need
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I need a channel that explains "how" and "why" you do certain computations. They all pretty much say, "this is what you do, this is what you get." It assumes you know certain things that you don't. Thank you for the time and effort you put into this. I just need a channel for someone who is seeing this subject for the very first time.
I absolutely love your passion! Thanks for doing what you do!
My pleasure!
Very great sir ❤
Perfect summary before my first Calc test! Clarified what I had already figured out myself Perfectly!! Thank you so much!
The comment on form was very helpful too!
This was so helpful! Sometimes it’s nice for me to have the basics clarified!
Yeep
Even it's been 5 year the video is still amazing
Whoa! ! Algebraic key to unlock calculus. Factoring, expanding, common denominator, radical conjugate four computing nifty techniques.
Thanking you sir! !
You're most welcom!
The same person who comments in every video i watch ❤
For the last one, x-4 = (sqr x-2)(sqrx+2)
I’m literally crying, this vid helped me so much! Thnx to you Dr. Trefor!
Thank you so much! You help me more than my own maths teacher!
in fact you have really made my day great. God bless. i will be happy to get in touch with you sir
In the last one, could you not have recognized that the denominator is a difference of squares and if you factor it as such then terms cancel?
Clear! But I found your videos on LaTeX were a bit too fast for my brain. Maybe I just need to do the same thing on my computer. I still appreciate them.
this video has taught me more in 7 minutes than my entire semester in calculus
When I factor, don't I change the domain or range of the function implicitly?
Indeed. But a limit doesn't care what happens AT the point, only around it.
@@DrTrefor👍🏻
Thank you for this
Very enjoyable thanks
Thank You Sir
Great Sir
Quick question: Why did you only use the positive root of 4 in the final evaluation step. If you used both roots - I.e. +/- 2 then you would get 2 solutions: 1/4 and +Inf, making the limit “DNE”?
sqrt(x) always means the non-negative root. If you want both you have to write ±sqrt(x).
Sqrt(4)=2. There is no others solutions
I imagine it is assumed that the function is only defined for the reals.
Nice sir 😊
Nice guys 😊👍👍👍
Why are we allowed to for example do x^2 divided by top and bottom since 0^2 is 0 and we would be dividing the top and bottom by 0. Isn’t that illegal?
What you are dividing with is not exactly 0. We are seeing where the function's value approaches when plugging a number just close to 0, like 0.0000000000000000000000000000000000000000000000001 or -0.0000000000000000000000000000000000000000000000000001, see how close it is? Its squared is even smaller, like 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001, but still not equal to 0. So you can divide by x^2 without breaking any math rules.
thank you sir..........
I always use *L‘Hospital Theory* if the result is 0/0
how do the terms cancel in numerator of no 4
plzz help
Waiting For Many Video's
What if I get trigonometric functions ????
Bastion main???
Bonne vidéo
dierectly we can use l hospital rule
nice.!!!1
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L'Hopital!
@@DrTrefor Aahh, I see! Nice tricks!
I must say nice if i understud it😂
STEM PA
Dont use lopitals rule because u r using limits to solve limits its a scam if you think on it 😂😂. If you dont care about scam then use it freely with all rules known about how to use it😅
you can use L'Hopital's rule only during 0/0 or infinity/infinity forms cuz the 0/0 is actually not exactly 0/0, the numerator and denominator maybe just greater than 0 or smaller than 0.
Why this video has korean substitles
Same question 😅
Righf 😂😂😂😂😂
w rizz
Ugh, I was following fine and now I have to look up what factorisation is.
Or what algebra is. How could you possibly get to calculus and not know that 😮
@@triple_gem_shining When you're self taught, you inevitably miss things. I know factorisation now, needed it for eigenvectors.
More efficient to find the LCD in part 3.