For 9, it's a bit tempting to first evaluate the e^(-x) terms to 0 then cancel e^(x)/e^(x) to 1. That is not rigorous, but gives the right answer in this case. Going forward, could you show an example where getting rid of a term that appears to go zero early on like that actually gives the wrong answer?
For limit 6, as x goes to infinity(and so does what is inside the square root), you could just add a +1 inside the square root, getting sqrt(x^2+2x+1), which is just abs(x+1), that, because x goes to -inf, becomes -x-1, so the original limit is reduced to x+(-x-1), so -1, which is the same result as you got. Btw it can be proven that the difference between sqrt(ax^2+bx+c) and sqrt (ax^2+bx), where a, b and c are constants, goes to zero as x goes to infinity.
Hang on! In example 6 are you saying sqrt(x^2) for negative x is negative? You could take either the positive or the negative sqrt but why preference the negative? The resulting limit is the same anyway so it doesn't matter in this case.
Please explain hypergeometric series and finding them when they're solutions to integrations, as in ∫tanⁿ(ax)dx, which, according the integral table involves a hypergeometric series.
20:06 Wait a minute... Functions can go to hell ?!
First time I ever saw a good explanation of the Squeeze Theorem. Thank you!
the best video I've seen on this concept, thank you
Esse canal tem um ótimo conteúdo. Parabéns pelo trabalho!
Obrigado :)
For 9, it's a bit tempting to first evaluate the e^(-x) terms to 0 then cancel e^(x)/e^(x) to 1. That is not rigorous, but gives the right answer in this case. Going forward, could you show an example where getting rid of a term that appears to go zero early on like that actually gives the wrong answer?
Excelent video
I think I learn (or possibly re-learn) something new in every video.
For limit 6, as x goes to infinity(and so does what is inside the square root), you could just add a +1 inside the square root, getting sqrt(x^2+2x+1), which is just abs(x+1), that, because x goes to -inf, becomes -x-1, so the original limit is reduced to x+(-x-1), so -1, which is the same result as you got.
Btw it can be proven that the difference between sqrt(ax^2+bx+c) and sqrt (ax^2+bx), where a, b and c are constants, goes to zero as x goes to infinity.
brilliant exercises thank you so much ❤
You're so welcome!
Another way of saying two wrongs might make a write is: "my exes cancel out nicely"
Hahaha
Hang on! In example 6 are you saying sqrt(x^2) for negative x is negative? You could take either the positive or the negative sqrt but why preference the negative? The resulting limit is the same anyway so it doesn't matter in this case.
18:06 - For a spiltsecond I thought we had to call an exorcist 🤣
Hahahaha
Please explain hypergeometric series and finding them when they're solutions to integrations, as in ∫tanⁿ(ax)dx, which, according the integral table involves a hypergeometric series.
Thank you Im now more confident for the AP exam
شكرا استاذ 🤍god jop
Thank you ♥
I liked the 7th limit
Thx professor,I follow of the Iraq
as always,it was beautifuly well explained...tnx DR.Peyam:)
so the squeeze theorem is just for the limit as x approches infinity or approches a number like c?
x can approache any value. You can go on Khan Academy they explain well
خوشحال شدم دیدمت
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Can we use Laurent series expansion at x=-inf for the sixth limit?
Hahaha, that’s a fancy way of doing it
@@drpeyam yeah) but it works easier for computing algorithms)
18:04 "bleaaaargh..." in 3...2...1 🤭
It was my birthday the day this video was released
Happy birthday!!! Your birthday is on pi-day? So cool!
👍👍👍👍👍👍👍👍
0:00.0000000000000001 sec
Why didn't you make a pi day special?
No time :(
Dr Peyam
Someone is worse. He didn’t even have a video for today.
blackpenredpen Stressful times :(
Dr Peyam yea
❤️❤️😍
Λ Terminusfinity Symbolfinity Inpredictafinity Instafinity Corrupfinity the intended recipient please b vf it and notify the
👍👍👍👍👏👏👏👏👏
number 5, i think u forget sqrt(9) .. is ±3 ..
sqrt(9) = 3
@@drpeyam hmm .. i think sqrt (9) =±3 .. but np .. nice content ... auto sapskrep 🤣🤣
No, sqrt(9)=3, sqrt(x) is always a positive number.