Quotient Rule vs. L'Hospital's Rule

Derivative of cos(x)/(1-sin(x)) vs. Limit of cos(x)/(1-sin(x)) as x goes to pi/2, Example of Quotient Rule vs. L'Hospital's Rule!

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blackpenredpen | 曹老師

[catholic_zoomer_bro]

Chen Lu, Prada Lu and now Kochen Lu.

Lol

[msolec]

7:32 NO NO NO NO!!!! Sin x cannot tend to 1+ EVER!!! The angle is (pi/2)+ but sin of that is still 1-.

[kruksog]

Wow, this is the first time I've actually tried the problem beforehand. You've really shined a light on how much my calculus skills have been neglected.

[ssdd]

6:53 shouldn't it be 1^- since sin(π/2)^+ is less than 1

[raghothamvaidya]

Thanks alot! I was applying quotient rule even in lim

[PISAGORAMA]

Hi, i have a limit question can you solve this ( lim x>infinity lnx to the lnx power)

[jimmorrison]

You can also solve the limit question without the use of Lhospital's rule.
Multiply both the numerator and the denominator by (1 + sin x) and you get (1 + sin x) / cos x and from here you get 2 / 0- and that is negative infinity

[juliocesar]

0:50 ready to bed and this bad boi appears. Can't sleep now, isn't it ?

[holyshit]

We dont need L'Hospital rule to calculate this limit
If we express trig functions as functons of half angle some cancellations will appear
and we will get lim x->pi/2^{+} tan(pi/4+x/2)
By the way this trig function reminds me substitution suitable for trig integrals

[canimotivateu]

Thanks from india i have this confusion from long time. And now clear

[ostdog]

Thanks for uploading more often youre my favorite math channel

[semiawesomatic]

Could you derive the quotient rule using the product rule?

[anupghimire]

In second problem use L hospital rule again
=X tends to (π/2) (cosx/-sinx)
So you will get:
=Cos90/-sin90
=0/-1
=0
I wonder how -infinity comes. 🧐

[shandyverdyo]

I just still wondering between L'Hospital's Rule or L'Hopital's Rule. Which one is correct? And how do i pronounce it? I hope somebody tells me.

[ilyaz]

Watching this video in Argentina while waiting for the Twilight, so cool :)

[atmonatmon]

Shoot a video about what is t: a ^ b = b ^ a * t

[blanks]

For the second one I multiplied by the denominator's conjugate first, so I got
lim (cosx)(1+sinx)/(1-sin²x)
x→π/2
three lines later, I got 2 as an answer. Did I do something wrong?

[pholioschenouda]

We haven't got a number theory problem in a while...
If you can make a video about non-extremely complicated number theory ones, it would be great
#BPRP_Love😍

[justdusty]

l'hopitals rule is nice and all but to whomever is reading this comment avoid using it when the derivatives look like they're complicated.
Learn how to manipulate taylor /maclaurin series effectively to evaluate limits

[shadyknopfler]

It's called "De L'Hôpital"