amazing

why did -2 become -4 when you isolate 1/2 from the absolute value?

This is helpful as always

what is y = lnx

So essentially: reframe it as an inequality, where the harmonic series is bigger than another series where each element n is rounded down to the next power of 2. This means that for every value 2^n, there exist 2^(n-1) elements that correspond to that value and which therefore add up to 1/2. Thus the series is *at least* as big as 1/2 added to itself an infinite number of times, which is a divergent value. Therefore the series is divergent. QED

What if we have two square roots adding together or subtracting one from another in the limits? Is it harder to prove using epsilon-delta definition? Please let us know.

It is addition that’s why, if it would be multiplication it would never 😅

While the formulas for the sequence may be correct, there's actually infinitely many possible formulas. This is why you have to specify what kind of sequence is it. Is it arithmetic? Is it geometric? And things like that

Good Sir. Can you also make a video how to get the domain and range of a square root. Like √x²+12 or √x+3/12 please

im confused. is the 1 always constant in the numerator when dealing with derivatives of natural logs? or this just applies to this function with x + y?

Thankyou

Je t'adore

thank you kind sir, taking calc 2 as a 4.5 week summer course and its rough

for the students I just point out the the Leibnitz notation has the 'virtue' of being open to some abuse i.e. switching from an 'operator on functions to 'differentials'-interpreation, when conveniant

String

0:56 waste of time ...

Use the chen lu

Very Useful thankyou bro !! I love your video

I don’t understand. I’ve never really seen it written like that, but who wouldn’t instantly understand the notation? Extremely straightforward

Couldve said that the reason of the sequence is greater than 1/2 so it diverges, extremely simple to understand

w vid

@bprpcalculusbasics what if I have a function, let's say x^2 and I want to apply the chain rule with another variable, let's say, u? I mean, df/dx = 2x but df/du = 0 because there's no u! And what happens with du/dx? I think cannot be 0 because otherwise we are saying, with that formula, that df/dx = 0! (exclamation mark, no factorial 😄)

I think there are other ways to describe what df/du mean in this context. df/du is actually a function with u as parameter to the function. u in this case is just a variable that can influence this function df/du. Let imagine f(u)=u³. df/du=3u². We can also express df/du as f'(u). Which means the input to the function is still u. In other words, this function is about the function of a rate of change as u progresses to the right. (i e increases). They want to monitor the output of function f(u) together with f'(u) with only ONE single variable that is u. So that is why the terminology of "with respect to" mean. df is the change of output of f(u) when let say u=0 and u=1. du is the change of the parameter u itself , can be calculated du=1-0 =1. It will be much clearer if you can plot a table and/or draw the shape of the graph. [ u ] [ 0 ][ 1 ] [ 2] [ f(u) ] [ 0³ ][ 1³ ][ 2³ ] [ f'(u) ] [3*0²][3*1²][3*2²] [ df ] [1³-0³][ 2³-1³] [ du ] [1-0][2-0] Then repeat this step with du/dx By letting function u(x) as some function that you would like , then try to multiply df/du with du/dx do you get df/dx?

If you use the concept of differentials, e.g.; dy and dx, then is it not technically correct that dy/dx can be thought of as a fraction since it is the ratio of the differentials dy and dx?

There’s a whole lot of answers with smart and reasonable arguments. Personally, last I checked, 1/3rd in decimal form wasn’t infinity.

Very well done. Thank you so much. I love this stuff.

I don't get it there isn't a limit because it doesn't approach a number ±inf isn't a number so the limit doesn't exist

X approaches 1 but never actually gets there, so everything plugged in is a real number ultimately. That's what limits are about, right?

At 7:30 why didn't you have to differentiate N wrt to ds/dt?

i know this dumb but i really want to know what is going on here

Why are you holding a pokeball so that when we faint from math you can capture us?

jaccobian matrix proof please

0.999....=lim_x->inf (1-(1/10^x))=1-0=1

Don't know why, but after 2s I saw, that this diverges and therefore hasn't a value.

C. At least for the others they are trying to integrate

I put this on WolframAlpha and got the same result. 4.4*10^72 seconds

In France, in the equivalent of the SAT (le bac) we have to present an oral about one of our two principal subject, and you just convinced me to present my oral about "How mathematics can help doctors to find out if you have a problem with your back"

A graph could've been helpful. The limits don't converge

2:34 why that need to times x?

I thought B had to do with magnetic fields. I have no clue as to what B and N refer.😢

I don't get it, why negative divide by negative is equal to negative?

Physics rotational dynamics

I am loving this mechanics video series. 😍

This video is pure entertainment. ✨

I don't know how well you know how to teach other aspect of math..but when it comes to math.. i give it to you🎉🎉😊😊

Lol I was stuck on this problem thx 😅