Hi Math Sorcerer: Could u explain the following? Prove Lim x tends to infinity 4x2-3x+2/8x2-6x+1 =1/2 Tried to understand it with the help of someone else, it’s difficult to clearly understand. Thank you
take x2 common on both up and down so that it becomes x^2(4-3/x+2/x^2)/x^2(8-6/x+1/x^2) cut x2 put infinity in x all with /x becomes 0 only 4/8 remains which is ur answer hope it helps
U r right but u should add one more step at the end X^2>y^2 THEN WE CANT say directly that x>y it is mathematically incorrect Correct statement is |x|>y it means xy So, here |a|+|b||a+b| But |a|+|b| is always positive so first one is wrong so, |a|+|b|>|a+b|
at 02:36 if you take the square root of an inequality shouldn't you take into consideration also the possibility of abs(a) + abs(b) =9 x could be greater than 3 but it could also be smaller than minus 3.
Interesting video> Can you prove it with the axioms O1-O5? That's what I have the most trouble with. Also can you prove the triangle inequality geometrically? I'm in first year math, so I have a ton to learn!!! Thanks for the video.
Great video! What happens with the +/- when you take the square root at the end?
6 років тому+1
He is using a property of the absolute value which states that, for a real number x, the absolute value of x equals the square root of x squared " |x|=(x^2)^(1/2) ". When he takes the square root, he is doing the square root of a squared number, so it is therefore equal to the absolute value of that number, and because that number is positive you can forget about the absolute value.
*thANK you* I was look for this in the textbook and I was just confused what they were referring to The Math Sorcerer comes to the rescue once again! :)
I understood the proof as you showed it, but I just really wanted to know in which cases |a| + |b| > a + b, because as far as my small brain can imagine, they are always equal.
@@纃 What if either a or b is negative. Then a+b will always be smaller than positive a + positive b (i.e., |a|+|b|). Draw a number line. Take a look. Also, -a+-b is always smaller than a+b since it is to the left of a+b. Any number to the left of a number is always smaller.
+The Math Sorcerer Wow! It took me so long to get this annoying inequality! I shall be forever thankful. As I noticed, the tricky part was at the 2|ab| ≥ 2ab.
If somebody tell her or his life got ruin, what about the unbreakable mind. If only one part of your body, soul or psyche are heal, you can build your whole body, soul and psyche healed like that only part as building ground spot. Identity analyses can be for more reasons than narssissmic personality. Or to find some great in you. It can be the oposite, to discover what have make you miserable. The first result isnt always the right.
I've been watching the playlist and I'm learning a lot from these videos. I'm new to this and am just learning it on my own. I was wondering if the following is a valid proof: |a+b| = |a+b + b/2 - b/2|
thank you so much! I was so discouraged when my teacher just told me to memorize this property. Thanks for helping me out!!!
I believe you still need to look at three cases: a and b have different signs; a and b are positive; a and b are negative.
Thank you .
I was seriously about to drop my Advanced Calculus class .
This series is incredibly helpful and well-explained.
Subscribed.
Hi Math Sorcerer:
Could u explain the following?
Prove
Lim x tends to infinity
4x2-3x+2/8x2-6x+1
=1/2
Tried to understand it with the help of someone else, it’s difficult to clearly understand.
Thank you
take x2 common on both up and down so that it becomes x^2(4-3/x+2/x^2)/x^2(8-6/x+1/x^2)
cut x2
put infinity in x
all with /x becomes 0
only 4/8 remains which is ur answer hope it helps
U r right but u should add one more step at the end
X^2>y^2 THEN WE CANT say directly that x>y it is mathematically incorrect
Correct statement is |x|>y it means xy
So, here |a|+|b||a+b|
But |a|+|b| is always positive so first one is wrong so, |a|+|b|>|a+b|
You just expanded it and then recondensed it? What was proven
That's how they behave 😂
Wow ! ... Wake up
I think you didn't understand clearly. IMHO.
It was a good proof what you on?
Quick and straight forward, nice. Subscribed!
Super helpful thank you!!! Quick, clear, and easy to follow!
when proving 2ab
I have a question, how do we know that the absolute value of x is greater than or equal to x ?
Thankyou sir for good explanation of this particular concept!!
Thank you! You explained better than my textbook did!! I am new to your channel and saw this vid and subscribed! Thanks, Sorcerer!!!
short, straightforward, nice done indeed
Thanks in advance. Could we generalize triangle inequality for polygens?
You're the most recent comment so im going to ask u, Just because /a/ is >= a and for b does the equation change from = to >=?
at 02:36
if you take the square root of an inequality shouldn't you take into consideration also the possibility of
abs(a) + abs(b) =9
x could be greater than 3 but it could also be smaller than minus 3.
Wow, this is really ingenious! Thank you for making this video!
You are welcome!
When you square root both sides, does this not create multiple solutions with negative roots? Anyways great video!
Up
can you tell me how to derive this inequality from the orignal inequality in the video ------> |a-b|>= |a|-|b|
This is one concise explanation and it,s not even the best part about it😅. Thank you
Very nicely done. Thank you so much!
Thank you so much for posting this!
Thanks for the nice proof!
Interesting video> Can you prove it with the axioms O1-O5? That's what I have the most trouble with. Also can you prove the triangle inequality geometrically? I'm in first year math, so I have a ton to learn!!!
Thanks for the video.
Grazie mille per questo video, short e anche facile da capire
Both values are equal ... How ?
Please give one example
Wow, i didn't think that it would be this simple !
I did this in my exam and my teacher didn't give full marks. I got 2/5.
why?
😂😂
it helped me so much..thank you
Great video!
What happens with the +/- when you take the square root at the end?
He is using a property of the absolute value which states that, for a real number x, the absolute value of x equals the square root of x squared " |x|=(x^2)^(1/2) ". When he takes the square root, he is doing the square root of a squared number, so it is therefore equal to the absolute value of that number, and because that number is positive you can forget about the absolute value.
Beautiful!!!
How to find proof goal.plz ans this question..?
what about doing this case by case in terms of whether a and b are positive/negative??
What about not doing that
@@triton62674 what about not doing this and that
You can do that too. That requires 3 cases. But I don't think that's suitable to do in an exam. That might take longer unless you have a lot of time.
It bothers me that in the Grammarly ad, ShakesPeer was never corrected and the narrator still said "much better".
Ikr
Perfect demostration im in first of industrial engeneer and it is helpful
awesome!!
*thANK you* I was look for this in the textbook and I was just confused what they were referring to
The Math Sorcerer comes to the rescue once again! :)
Many thanks for this good video.
👍
what ! i am crying. thank you sm for this
Nice work 🎉
you deserve more views :)
:)
Well explained. The proof I read doesn't even come to this conclusion
Thank you so much, now I understand.
Can you help with a question please?
I understood the proof as you showed it, but I just really wanted to know in which cases |a| + |b| > a + b, because as far as my small brain can imagine, they are always equal.
Because a+b>-(a+b)
@@纃 What if either a or b is negative. Then a+b will always be smaller than positive a + positive b (i.e., |a|+|b|). Draw a number line. Take a look. Also, -a+-b is always smaller than a+b since it is to the left of a+b. Any number to the left of a number is always smaller.
Nice video 🤗but can't able to see clearly
not understanding at 1:35 how does it go from being equal to being greater than or equal to ?
it's because |a| >= a and |b| >= b, so you can drop the | | and insert >=
@@TheMathSorcerer ah I see, thank you 🙇♀️
The Math Sorcerer why is |a|>=a and |b|>=b?
Elyne Khoo because a and b can be intrinsically negative but absolute value is always positive
@@elynekhoo if you don't know this, then you do not know what absolute value means.
+The Math Sorcerer
Wow! It took me so long to get this annoying inequality! I shall be forever thankful.
As I noticed, the tricky part was at the 2|ab| ≥ 2ab.
יהודה שמחה ולדמן
glad it helped!!
Good 👍
Thanks. A lot 👍
thanks ,,,helpfull
np:)
Nice!!!
(a+b)2 does not equal |a+b|2 .... why is no one saying anything ...
for all real numbers x it is true that |x|^2 = x^2, a + b is a real number, therefore |a+b|^2 = (a+b)^2
If somebody tell her or his life got ruin, what about the unbreakable mind. If only one part of your body, soul or psyche are heal, you can build your whole body, soul and psyche healed like that only part as building ground spot. Identity analyses can be for more reasons than narssissmic personality. Or to find some great in you. It can be the oposite, to discover what have make you miserable. The first result isnt always the right.
wtf, why is my profs proofs so much harder than this. It uses cases showing that X+Y
Wait, what? 🤯
Thhhank you very much finally I am understand will 😩💜
Yeah, but actually no.
Hi
Can you prove this
0 < x < 1 ⇒ 0 < x^2 < x < 1
nice
I've been watching the playlist and I'm learning a lot from these videos. I'm new to this and am just learning it on my own. I was wondering if the following is a valid proof:
|a+b| = |a+b + b/2 - b/2|
No, because you are already assuming that the Triangle Inequality is true when you wrote |a+b + b/2 - b/2|
Jiri would never
10/10 proof
Jiri sux
Watch out the thumbnail the vedio was different
nice!
Hi
Hi
What? I'm confused. What are we going to prove ? 😳
Skipped too many steps. This is a quick and dirty proof, but not a whole proof.
Frick Jiri