@@aaryavbhardwaj6967that isn't copying I guess? There are differences. Moreover I was eating so I had to do it with left hand which took me some time. Sorry if that causes any confusion. Have a great day!
My Calculus 3 class never had such interesting (and challenging) multivariable limits. I had never even seen a multivariable limit question that didn't approach the origin until I saw your videos. I had also never seen a multivariable limit question where the answer required the sin(x)/x limit or a parametric curve until this video. Awesome stuff!
I am not sure if many Calc3 students would just know that limit in Q3. I stopped and proved it using the definition of a limit - which is a cool and easy exercise, but in real life it would have been l'hopitals for me as well.
I’m assuming you are talking about the x = 0 case. That’s something you’d learn in calculus I. Since (1 - cos(x))/x is 0 that one would have been -1 * 0 which is still 0.
@@aaryavbhardwaj6967I know, but in this video 8:35 , why not ideal to do L'hopital's rule? When we calculate the limit of two variables along a curve, doesn't it become the limit of one variable? However, after watching several other videos from BPRP, L'hopital's rule was indeed the last option.
@@otekpreketek No in the e^x limit we can definitely use Lhopitals. It is just a direct way used by Bprp without differentiating. In the cos y limit, Lhopitals can be used but is not ideal as while u find d/dx fos cos the cos h-1/h appears so to differentaite that u have to know d/dx cosx = -sinx. This leads to a loop and has to be proved by geometry to which u can find various videos. So Lhopitals can definately be used but is not ideal in 2nd case.
6 ways of evaluating the limit of a multi-variable function: ua-cam.com/video/FJ-ofPVY5P8/v-deo.html
Timestamps
Q1:- 0:00 - 4:03
Q2:- 4:04 - 7:31
Q3:- 7:32 - 12:09
Q4:- 12:10 - 18:22
Q5:- 18:23 - 23:49
Q6:- 23:50 - 31:11
Q7:- 31:12 - 34:49
Q8:- 34:50 - 40:19
Up
@@aaryavbhardwaj6967that isn't copying I guess? There are differences. Moreover I was eating so I had to do it with left hand which took me some time. Sorry if that causes any confusion. Have a great day!
Sorry for being a bit rude
00:00 Intro
00:36 (x^2+y) /(x-2y)
04:05 |x|^|y|
07:33 (e^x - cosy)/(x-y)
12:10 (x^2 y)/(x^4+y^2)
18:24 xy/(x+y)
23:51 (√x+√y-2)/(x+y-2)
31:12 (xsinx)/siny
34:49 (x y^2 z^2)/(x^3+y^6+z^6)
40:07 Outro
Hi bprp, Here are the timestamps. BTW it was a very nice one. ❤
Up
Thank you!
@@bprpcalculusbasicsWelcome sir
Could anyone make the timestamp for this video? Thank you!
I don't have the patience for that lmao😂😂
Outsourcing at its finest
My Calculus 3 class never had such interesting (and challenging) multivariable limits. I had never even seen a multivariable limit question that didn't approach the origin until I saw your videos. I had also never seen a multivariable limit question where the answer required the sin(x)/x limit or a parametric curve until this video. Awesome stuff!
Like i saying always what a teacher wonderful
Number 7 is just amazing
Moments at 9:00 are so beautifull
I am not sure if many Calc3 students would just know that limit in Q3. I stopped and proved it using the definition of a limit - which is a cool and easy exercise, but in real life it would have been l'hopitals for me as well.
I’m assuming you are talking about the x = 0 case. That’s something you’d learn in calculus I. Since (1 - cos(x))/x is 0 that one would have been -1 * 0 which is still 0.
For the 6th limit, can't we just take y=kx and apply l'hopitals? This approach also givez DNE for the limit
The first time during the premiere period!
Hi what abt in Q2 when x=0 can't y approach from 0- I.e. if 0 has neg power then the lim is ♾️?
It is |y| so the power is always positive
Thanks
@@Ninja20704,
When should we ideally use L'hopital's Rule?
0/0 Or ♾️/♾️ in single variable
@@aaryavbhardwaj6967I know, but in this video 8:35 , why not ideal to do L'hopital's rule?
When we calculate the limit of two variables along a curve, doesn't it become the limit of one variable?
However, after watching several other videos from BPRP, L'hopital's rule was indeed the last option.
@@otekpreketek No in the e^x limit we can definitely use Lhopitals. It is just a direct way used by Bprp without differentiating.
In the cos y limit, Lhopitals can be used but is not ideal as while u find d/dx fos cos the cos h-1/h appears so to differentaite that u have to know d/dx cosx = -sinx. This leads to a loop and has to be proved by geometry to which u can find various videos.
So Lhopitals can definately be used but is not ideal in 2nd case.
Hi can anyone pls twll me that why
Integral of tanx= ln|sec x|+C
But shouldn't integral of tanx = -ln|cos x|
secx is 1/cosx and by log properties ln(secx)=ln(1/cosx)=-ln(cosx). So they are the same
You are late :)) I just finished my exam. Hope it'll be alright. Or perhaps I am late cause you posted this 2 weeks ago😂
no entiendo que hablas pero veo tus videos son interesantes jajaja :D