L'Hôpital's rule example 2 | Derivative applications | Differential Calculus | Khan Academy

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L'Hôpital's Rule Example 2
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Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.
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Опубликовано:

8 окт 2024

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Комментарии : 68

@faddeen2255 2 года назад

a video from 12 years ago still helping me. Thanks khan academy

@mrkoliverie 11 лет назад

Thanks dude for posting these videos it has really made me appreciate math and see the beauty of it. keep it up

@Frankenberry84 11 лет назад

You're my Calculus hero.

@ManinderjitG 13 лет назад

Instead of factoring out an x-sqaured, you can also look at the coefficients of the ones with the x to the largest exponent. Take those coefficients and you get your answer. For instance, in this problem, Step 1) this limit is being evaluated as x approaches infinity, Step 2) x-squared is the "largest" exponent, there is an x-sqauared on the top and bottom, therefore, Step 3) I can take those coefficients out and get my answer. It's a neat trick but it is also a good idea to check your answer.

@jingyiwang5113 11 месяцев назад

Thank you so much for these amazing explanations!

@Daski69 10 лет назад

i'm confused... I mean it makes total sense that it would be +infinity over -infinity but it would also make sense that it should be -4/3 since the 5x wouldn't matter as x->inf. and the 1 in the denominator shouldn't matter as compared to the -3x^2 when is that latter proposition the case instead of +inf/-inf? I know that it's also a very common thing edit: lol, just noticed that that's exactly the answer that we got as the video proceeded. I guess I was just thinking about a shortcut

@frozenruby23 11 лет назад

I like your voice, and thank you so much!

@finwasfound Год назад

last time we had a x approaching infinity limit problem all we do is find the biggest growing terms on numerator and denominator which were x² and since theyre growing at tbe same pace they cancel out leaving us with 4/-3 or -4/3

@milopmendozaful 11 лет назад

Thanks man. You're awesome.

@asemnafiz 11 лет назад

I like his videos even before they start.

@jettubes1 13 лет назад

very good, your channel is my classroom... :D

@ijohara96 8 лет назад

I'm gonna get an F

@peoplelikegamers5024 8 лет назад

hahaha... don't say that man 😂😂

@lensmurf7039 8 лет назад

+Johara laughtrip

@xitsxjustxmarix 6 лет назад

relatable

@arunkenta 11 лет назад

These videos are great. Thanks alot

@prasoon-manandhar 12 лет назад

sallu bhai thank you

@kathryniii 12 лет назад

thank you!

@roopperlanna8216 9 лет назад

ขอบคุณมากครับมีแปลไทยด้ย thanks a lot. have translate it is very good. thank you very much

@Saul1913 6 лет назад

couldn't we also just use leading coefficient since both denominator and numerator both have x ^2, so it will equal 4/-3 = -4/3

@amircanto5416 5 лет назад

Well, given that this comment is one year old+, you now might have forgotten, but the objective is to solve by using L'Hopital. I still think Sal should have looked for a problem that could not be solved without L'Hopital

@maxbretschneider6521 3 года назад

He also said that you should be able to solve it another way

@naweedbabakarkhail5210 6 лет назад

so i'm assuming that this is the general formula for finding any limit. But what if the limit does not exist and you end up doing L'hopitals rule perhaps endlessly to no avail? How do you know the limit does not exist?

@apestogetherstrong341 Год назад

Delta epsilon definition, probably

@odefeoberabor7597 9 лет назад

Good explanation !!

@ny1fanta 14 лет назад

cool. do more cal 2 problems=]

@DGVFX 13 лет назад

Does watching this in 720p HD to my 42" TV and 5.1 home cinema speakers makes me a nerd?

@xx420xxyolo3 8 лет назад

720 lol try 4k

@naweedbabakarkhail5210 6 лет назад

lol it was 7 years ago so that's pretty crazy for 7 years ago aha

@arunkenta 11 лет назад

Its because the denominator is being subtracted by a positive number. And the numerator is infinite beacu x just takes infinite

@hossein1413 14 лет назад

WOW !! thats nice

@msharimk2450 6 лет назад

satisfied , thanks

@Hellboywillnevercome 11 лет назад

thanks alot!!!!

@happy321hh 13 лет назад

Why didnt we use the qoutient rule?

@batuleiddy4949 4 года назад

You are awesome

@kangarooisaac 11 лет назад

How do we decide if we do the limit as it approaches 0 or as it approaches infinity?

@lensmurf7039 8 лет назад

It depends if your professor gives you a limit of infinity or 0

@mrkoliverie 11 лет назад

hey sal could you have rationalize the denomerator?

@koreanmilkman 10 лет назад

as always, good stuff

@anab956 3 года назад

🙀Awesome 😌

@danteeep 11 лет назад

thanks a lot again !!!!!!

@nondumisosibiya7755 7 лет назад

how come the quotient rule does not apply because we are looking for derivatives of one function over another function ?

@ColdFuse96 4 года назад

What if the exponents dont match?

@Nguyening_music 13 лет назад

@happy321hh because he just wants to show you what l'hospital rule, he also use the extraction of x trick, or simplifying trick, but since this is a l'hospital rule lesson, so that's what he's using haha. also quotient rule would still pretty crappy lol

@johngrosjean9664 7 лет назад

Why don't you use the quotient rule?

@saipandala6637 6 лет назад

numerator and denominator are separete functionsf(x) and g(x), actually f'(x) and g'(x) are to be done separately and should find f'(x)/g'(x). here he done direcctly so you got confused for quotient rule.

@GM.Nobody 4 года назад

If you used quotient rule you still have x remaining thus, still infinity over infinity

@hwin1418 10 лет назад

So you derived (4x^2-5x)/(1-3x^2) and then did it another time to get -4/3? I thought it was f'(x)/g'(x) = L but in this case it was f''(x)/g''(x) = L?

@Mrshazeb7 10 лет назад

Keep deriving until you get a constant for L.

@mohammedshaaeli154 6 лет назад

Lim f(x)/g(x) = lim f'(x)/g'(x) = lim f''(x)/g''(x)

@shobhit2197 7 лет назад

Is L'Hopital rule allowed in High-school tests?

@loydbriski8313 5 лет назад

Should be

@Antroz0197 12 лет назад

@chinotovar You will succeed in college. :D

@maornativ5493 6 лет назад

? How do you pronounce it ? to multiply by a congigit

@vishal7244 14 лет назад

i knew it already

@archieh.jelbert7866 7 лет назад

what level is this? what age do people learn this and what subject

@stephentian6518 6 лет назад

Archie H. Jelbert This is AP Calculus AB. You take it after trigonometry. And the class you take after should be AP Calculus BC. It's technically a college class, given that it's a AP course, but a lot of people take it in their junior or senior year in high school. Math is not my strong suit so I'm currently taking it in my senior year in high school. I'm 18.