In this video showed how and when to use L'Hopital's rule ffor taking limits
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Пікірлер: 38
@icafe364855 ай бұрын
How well-mannered you are and how patiently you teach❤
@PrimeNewtons
5 ай бұрын
I appreciate that!
@tomtomspa6 ай бұрын
the reason you can bring the limit at exponent is not because e is constant, but rather that the exp function is continuos.
@komalshah15358 ай бұрын
This person is outstanding teacher. So much enthusiasm for maths is unheard of .
@calebo88822 жыл бұрын
just stumbled on your account while studying for my midterm and man you're such a help! i saw one video explaining limits approaching infinity and it was EXACTLY what i needed at that instant. i was stuck somewhere else and searched "prime newtons l hopital" and this video came up and now i understand l hopitals rule kind of. thank you so much! and i hope your day is better knowing that youve helped a random stranger across the world.
@ianrobinson85185 ай бұрын
Very clear demo. And unexpected answer! I would have eased the approach by setting the expression to y and taking logs before applying l’Hôpitals rule. Then exponentiate once -1/2 is derived. It’s also not necessary in practice to keep writing the limit or derivative expression on top and bottom each time. Just go direct. But I accept you’re seeking clarity for demo purposes.
@joshandseb Жыл бұрын
"that's a terrible line but we'll still accept it" LOL Your ability to make learning these subjects enjoyable is truly commendable. I want to express my sincere gratitude for your outstanding videos, which are incredibly clear and concise. Whenever I discover that you've covered a topic I'm interested in, it brings me great anticipation and excitement. Thank you so much for your valuable contributions.
@PrimeNewtons
Жыл бұрын
🤣 I appreciate the support 🙏 ❤️
@rudorwashemuzangaza19783 ай бұрын
Sir,you are just too good!!!much blessings!
@codeescape98 ай бұрын
00:08 Limits requiring L'Hopital's Rule 01:55 Applying L'Hopital's Rule to find the limit of the given expression. 03:40 To evaluate the limit, we use L'Hopital's Rule. 05:56 L'Hopital's Rule can be applied to rational expressions if the limit gives zero over zero. 07:53 L'Hopital's Rule allows you to differentiate the top and bottom separately when you have a rational function with a limit of zero over zero. 09:47 L'Hopital's Rule allows us to find the limit by differentiating the numerator and denominator separately. 11:54 The application of L'Hopital's Rule is discussed in finding the limit as x approaches zero. 14:23 The limit of negative secant squared x as x approaches zero is e to the negative 1/2.
@keithrobinson29416 ай бұрын
Those are very large ees! Love the video. Your eeeexplanations areee aweeesomeee!
@dimakatsolanga9606 Жыл бұрын
hilarious😂...good job sir🙌
@MziweneleDikoАй бұрын
You're the best sir you deserve an award 👏
@samsonsisay47629 ай бұрын
You're just awesome!
@user-kl6dr9wm3e3 ай бұрын
Wow you really know how to explain
@spaceshipastro2 ай бұрын
thank u!! it went easy
@cherryisripe31656 ай бұрын
It’s a beauty!
@user-fp7lb4nw9h6 ай бұрын
I love you my brother . And l like your study . Sr
@Emma-ki3fv7 ай бұрын
thank you!
@bogusawsroda37475 ай бұрын
Super
@surendrakverma5553 ай бұрын
Thanks Sir
@MakuSmret4 ай бұрын
Cool
@ahmedabdelkoui37903 ай бұрын
From {lim(sinx/cosx)}/{lim(2x)}=lim{sinx/(2xcosx)}=lim{(sinx/x)(1/2cosx)=1/2 because lim(sinx/x )=1. We clearly understand lim in this limiting case when x tends towards zero. Consequently, without going to the tangent and the secant, the limit sought is e^(-1/2)=1/√e.
@klementhajrullaj12223 ай бұрын
You can do it even more briefly, without using the second derivative, because the limit when x goes to 0 of tanx/x is the same as the limit when x goes to 0 of sinx/x, so equal to 1, therefore, all the limit will be: e^(-1/2)=1/e^(1/2)=1/Ve=Ve/e.
@nabilahmed7534
3 ай бұрын
Yeah
@ACBis23 күн бұрын
What If we use log instead ln?
@L1merencer6 ай бұрын
Hey i have a question. If i replace the e and natural log to another constant and another logarithm, does the answer change?
@redpepper74
4 ай бұрын
It wouldn’t because when you differentiate log_n(x) you get 1/x divided by the constant ln(n). Then, because that constant is in the exponent, you can get rid of it by using the fact that n^(1/ln n) = n^(log_n(e)) = e.
@user-qx4wg5gs1x4 ай бұрын
Isn't limit of tanx/x is already 1, If yes, why extra step?
@tarciso21claudia286 ай бұрын
Optimus magister in hoc mundo !!!
@wafalsh81313 ай бұрын
Can we solve without L Hopital's rule ?
@subbaraoorugantiАй бұрын
Limit of tan x/x = 1 if x tends to zero
@billykim71794 ай бұрын
L'hopital is very powerful. but you don't need to use that here. there is another solution. in korea, we learn this problem like below. let cosx-1=t, then cosx=t+1, and when x->0, then t->0 (lncosx)/(x^2) =(cosx-1)(lncosx)/(cosx-1)(x^2) ={(cosx-1)/(x^2)}×{ln(t+1)/t}=-1/2 (because lim[x->0](cosx-1)/(x^2)=-1/2, lim[t->0]ln(1+t)/t=1) i am sorry i am not good at english😢
@Prphadgaming775 ай бұрын
Tanx/x = 1
@SmokalotOPott6 ай бұрын
That is the limit when X approaches 0 from the negative numbers, when X approaches 0 from the positive numbers, the limit is 1.
@brendanward2991
5 ай бұрын
But the function is symmetric about the y-axis. Replacing x with negative-x does not change it.
Пікірлер: 38
How well-mannered you are and how patiently you teach❤
@PrimeNewtons
5 ай бұрын
I appreciate that!
the reason you can bring the limit at exponent is not because e is constant, but rather that the exp function is continuos.
This person is outstanding teacher. So much enthusiasm for maths is unheard of .
just stumbled on your account while studying for my midterm and man you're such a help! i saw one video explaining limits approaching infinity and it was EXACTLY what i needed at that instant. i was stuck somewhere else and searched "prime newtons l hopital" and this video came up and now i understand l hopitals rule kind of. thank you so much! and i hope your day is better knowing that youve helped a random stranger across the world.
Very clear demo. And unexpected answer! I would have eased the approach by setting the expression to y and taking logs before applying l’Hôpitals rule. Then exponentiate once -1/2 is derived. It’s also not necessary in practice to keep writing the limit or derivative expression on top and bottom each time. Just go direct. But I accept you’re seeking clarity for demo purposes.
"that's a terrible line but we'll still accept it" LOL Your ability to make learning these subjects enjoyable is truly commendable. I want to express my sincere gratitude for your outstanding videos, which are incredibly clear and concise. Whenever I discover that you've covered a topic I'm interested in, it brings me great anticipation and excitement. Thank you so much for your valuable contributions.
@PrimeNewtons
Жыл бұрын
🤣 I appreciate the support 🙏 ❤️
Sir,you are just too good!!!much blessings!
00:08 Limits requiring L'Hopital's Rule 01:55 Applying L'Hopital's Rule to find the limit of the given expression. 03:40 To evaluate the limit, we use L'Hopital's Rule. 05:56 L'Hopital's Rule can be applied to rational expressions if the limit gives zero over zero. 07:53 L'Hopital's Rule allows you to differentiate the top and bottom separately when you have a rational function with a limit of zero over zero. 09:47 L'Hopital's Rule allows us to find the limit by differentiating the numerator and denominator separately. 11:54 The application of L'Hopital's Rule is discussed in finding the limit as x approaches zero. 14:23 The limit of negative secant squared x as x approaches zero is e to the negative 1/2.
Those are very large ees! Love the video. Your eeeexplanations areee aweeesomeee!
hilarious😂...good job sir🙌
You're the best sir you deserve an award 👏
You're just awesome!
Wow you really know how to explain
thank u!! it went easy
It’s a beauty!
I love you my brother . And l like your study . Sr
thank you!
Super
Thanks Sir
Cool
From {lim(sinx/cosx)}/{lim(2x)}=lim{sinx/(2xcosx)}=lim{(sinx/x)(1/2cosx)=1/2 because lim(sinx/x )=1. We clearly understand lim in this limiting case when x tends towards zero. Consequently, without going to the tangent and the secant, the limit sought is e^(-1/2)=1/√e.
You can do it even more briefly, without using the second derivative, because the limit when x goes to 0 of tanx/x is the same as the limit when x goes to 0 of sinx/x, so equal to 1, therefore, all the limit will be: e^(-1/2)=1/e^(1/2)=1/Ve=Ve/e.
@nabilahmed7534
3 ай бұрын
Yeah
What If we use log instead ln?
Hey i have a question. If i replace the e and natural log to another constant and another logarithm, does the answer change?
@redpepper74
4 ай бұрын
It wouldn’t because when you differentiate log_n(x) you get 1/x divided by the constant ln(n). Then, because that constant is in the exponent, you can get rid of it by using the fact that n^(1/ln n) = n^(log_n(e)) = e.
Isn't limit of tanx/x is already 1, If yes, why extra step?
Optimus magister in hoc mundo !!!
Can we solve without L Hopital's rule ?
Limit of tan x/x = 1 if x tends to zero
L'hopital is very powerful. but you don't need to use that here. there is another solution. in korea, we learn this problem like below. let cosx-1=t, then cosx=t+1, and when x->0, then t->0 (lncosx)/(x^2) =(cosx-1)(lncosx)/(cosx-1)(x^2) ={(cosx-1)/(x^2)}×{ln(t+1)/t}=-1/2 (because lim[x->0](cosx-1)/(x^2)=-1/2, lim[t->0]ln(1+t)/t=1) i am sorry i am not good at english😢
Tanx/x = 1
That is the limit when X approaches 0 from the negative numbers, when X approaches 0 from the positive numbers, the limit is 1.
@brendanward2991
5 ай бұрын
But the function is symmetric about the y-axis. Replacing x with negative-x does not change it.
12:12 (lim)(x→0) sinx/x=1