Very interesting and nice solution, but in the title it was not indicated to find approximate solution. But like 2.02 = 2(1+0.01), it's possible to calculate the real value without calculator: 5,079192.
Using a sledgehammer to crack a nut. This is 2.02^2 (2.02 - 4) + 3 =- 2.02*2.02*1.98 + 3 = -2.02*(2+0.02)(2 - 0.02) + 3. The difference of these squares is approximately 4 as 0.02^2 is negligible in comparison with the other terms. Thus the answer is approx -2.02*4 + 3 = -8.08 + 3 = -5.08.
It's funny, I never learned approximation in precalc or my early calc classes. Might've come in handy later when I had to come to grips with stuff like Newton's method.
@@Queen-be6md nice try with the straw man argument, but my disbelief clearly came from the fact that I have never seen derivatives taught without linearization. also, stop virtue signaling everyone knows that less resources allocated towards education is detrimental to the learning process. why do you think people from poor communities try and get their kids into the "nice white schools"? You're fooling yourself if you think that money and resources dont do anything for the schools and their students, but again that wasnt even my original argument.
@@Queen-be6md sure, but to argue as if money and resources aren't at least somewhat correlated with students and quality of education is just foolish dude. Again though, not really what I was trying to argue about but whatever since thats the only thing you read out of my entire paragraph.
@Luffy D Uchiha I suppose it depends on how comfortable a person is doing math in their head -- I didn't have a problem with 3 * 2 * 0.0004, etc., and if I had to guess I was able to get the exact answer in three or four minutes, which matches bprp's first run-through. Though admittedly I wasn't stopping to explain what I was doing to an audience. On the other hand it was early and I hadn't had my coffee yet so that probably slowed me down. Grouping "like" terms helped once I realized that everything stayed in its own set of two decimal places. My last calculation was -5 - 0.08 + 0.0008 + 0.000008 if I remember right, which wasn't too bad.
Hello, As a calculus 1 student, I was quite confused when you stated that dy is approximately delta(y), I previously thought that they were the same thing as in dy = delta(y). Could you please explain that particular point?
Not sure if this is the answer: do you know that calculus graph of lots of rectangles drawn under the curve? There is always a little bit of loss while drawing those. I always thought that was the difference between dy and (delta)y
it’s because Δy is the change in the y value from x=2 to x=2.02 but dy is the instantaneous rate of change of the y value at x=2. dy changes at every value from x=2 to 2.2
dy on its own is known as the differential, it is different from Δy. Δy is based off the change in y in the original equation and dy is based on dy = f'(x) * dx.
Because what would happen if a Pokemon came up while he was giving the lecture and he didn't have a pokeball to catch it? I mean he's got to catch them all.
Very interesting and nice solution, but in the title it was not indicated to find approximate solution. But like 2.02 = 2(1+0.01), it's possible to calculate the real value without calculator: 5,079192.
Using a sledgehammer to crack a nut. This is 2.02^2 (2.02 - 4) + 3 =- 2.02*2.02*1.98 + 3 = -2.02*(2+0.02)(2 - 0.02) + 3. The difference of these squares is approximately 4 as 0.02^2 is negligible in comparison with the other terms. Thus the answer is approx -2.02*4 + 3 = -8.08 + 3 = -5.08.
It's funny, I never learned approximation in precalc or my early calc classes. Might've come in handy later when I had to come to grips with stuff like Newton's method.
Estimation is an underrated skill definitely.
Dude there is no way they just skipped linearization in precalc. Where are you from some third world country?
@@l33tsn1per wow so in usa and europe all schools are top notch? mediocricy isnt exclusive of any country and youll find mediocre places everywhere.
@@Queen-be6md nice try with the straw man argument, but my disbelief clearly came from the fact that I have never seen derivatives taught without linearization. also, stop virtue signaling everyone knows that less resources allocated towards education is detrimental to the learning process. why do you think people from poor communities try and get their kids into the "nice white schools"? You're fooling yourself if you think that money and resources dont do anything for the schools and their students, but again that wasnt even my original argument.
@@Queen-be6md sure, but to argue as if money and resources aren't at least somewhat correlated with students and quality of education is just foolish dude. Again though, not really what I was trying to argue about but whatever since thats the only thing you read out of my entire paragraph.
I learned it as f(x+h) approx = f(x) + h*f'(x), makes it a lot easier to work with.
Pre-calc not calculus :) A = 2, B = 0.02, use the binomial theorem, get the exact answer of -5.079192.
@Luffy D Uchiha I suppose it depends on how comfortable a person is doing math in their head -- I didn't have a problem with 3 * 2 * 0.0004, etc., and if I had to guess I was able to get the exact answer in three or four minutes, which matches bprp's first run-through. Though admittedly I wasn't stopping to explain what I was doing to an audience. On the other hand it was early and I hadn't had my coffee yet so that probably slowed me down.
Grouping "like" terms helped once I realized that everything stayed in its own set of two decimal places. My last calculation was -5 - 0.08 + 0.0008 + 0.000008 if I remember right, which wasn't too bad.
I love your videos, Steve. Very educational! 👍
People who used Binomial and still got the same answer: 🤯
Mismatched paren colors at 3:29! Now you gotta redo the whole thing ;)
😱!!!!
U r right!!!! That’s going to bother me 😆
I mean that parenthesis color. You may have known that I am super picky about it.
Is it -5.079192? i get this by keep dividing x^3-4x^2+3 by x-2 and put x=2.2
I was finding such a fine explanation of these kind problems... Thank you very much 🙂
Also, *First Comment*
After watching this I have more respect for the inventor of calculator
This was truly amazing. Thank you for taking the time to share this. Very impressive!
Bro accidentally had a poke ball equipped with out noticing
Hello,
As a calculus 1 student, I was quite confused when you stated that dy is approximately delta(y), I previously thought that they were the same thing as in dy = delta(y). Could you please explain that particular point?
Not sure if this is the answer: do you know that calculus graph of lots of rectangles drawn under the curve? There is always a little bit of loss while drawing those. I always thought that was the difference between dy and (delta)y
it’s because Δy is the change in the y value from x=2 to x=2.02 but dy is the instantaneous rate of change of the y value at x=2. dy changes at every value from x=2 to 2.2
dy on its own is known as the differential, it is different from Δy. Δy is based off the change in y in the original equation and dy is based on dy = f'(x) * dx.
Thanks. I only know differential method, and a bit confused by linearisation method.
Super. Excelent.Thank You teacher.
1:29 *two* vs *two* point *two* is not *too* far away
Intended?
very cool, this video single-handedly reminded me why i love maths and inspired me to try harder for my exam in a month
The title is use calculus not calculator and I compute it to calculator
😆
This is soo interesting,shall try it out foshooo,Keep Growing
8:44 lol 😂
Robotics mantra: the Jacobian is the best linear approximation, but you're screwed if you have to compute it on a tight time interval
*what's good my boy*
The wow sound happened in my head when the values where the same.
understandable.
I've always wondered why it's DX or DY or DT or anything like that and not delta-y or the like. Don't they both mean the change in
Delta y means change in y whereas dy means very small change in y.
Delta is just a symbol whereas the other is an differential operator
i had my physics exam today and i forgot calculator at home...
i come back to see this
Why do you have a Pokeball in your hand?
Because what would happen if a Pokemon came up while he was giving the lecture and he didn't have a pokeball to catch it? I mean he's got to catch them all.
3 is guilty
Someone explain to me the pokeball please
hmm pen and paper will work
nah i'll stay with my calculator
Me be like: Ok 2.02 is almost 2 so this would be 8-16+3=-5
Don't use calculus use approximation
??????????????????
the kind of rudimentary problems i've recently practiced
I hate calculator!
Yes ... It's right ... *Calculus not calculator*
Thank you teacher