Rules are way faster than the definition,(if i want to be more efficient into solving the exercices i need to use them) but sometimes, as the case i posted i cannot use them. I just wanted to know why, I am not always going to use the same wrench (definition) cause in the end i would lose time.
hum... that seems kind of vague, i just wanted to know why in some cases i cannot calculate the partial derivates by the the rules and i need to use the definition: let me ilustrate with an example... (Lets say i want to calculate the partial derivatives of f(x,y) and f(x,y) is...
Homework Statement
Hi, this is a question that has been bothering me for a while. (Im in calculus II at the moment)
Why do i need to derivate some functions by definition and other times i dont? for example if somebody asks me to calculate the partial derivatives of a branch function in a a...
Sorry, I've been reviewing the steps and what i really meant to write as Step 1 was :Step 1- I know that (1/(an^(2) + 1) < 1/an . (i bugged the integral symbol on the previous post)
Step 2- Since Σ1/an and ∑(1/(an^(2) + 1) have just positive terms i can conclude by the criterion of geral...
Ok! i think i got it. Can anyone just say if this sounds like a reasonable answer?
They ask me to study nature of ∑(-1)^n/(an^(2) + 1) knowing that 1/an is convergent.
Step 1- I know that ∑(1/(an^(2) + 1) < 1/an .
Step 2- Since all the terms of the series in Step 1 are positive i can...
I know that if (bn) converges, (an) will also converge. So i know that Σ(1/(an^(2) +1) is convergent, However my problem is that the serie in question is Σ((-1)^n/(an^(2) +1) and since it has negative terms i can't apply that criterion. The same applies with bn. If i know bn is convergent...
I can't conclude nothing using the geral criterion of comparison cause it only applies to series with positive terms. The problem is that (-1)^n !
Im almost sure it converges but on the definition of this criterion it says it is explicitly for series with positive terms...
Oh sorry. yes i did, i notice that the terms are smaller. Are you saying that i can compare the serie
Σ 1/(an^(2) +1) with (1/an) using the criterion of geral comparison?
If an≤bn for n ≥ f then:
(1) -Σbn is convergent → Σan is convergent
(2) -Σan is divergent → Σbn is divergent
At a first...
1. The problem:
Ive been all afternoon struggling with this doubt. Its a bit more teoric than the rest of the exercices i did and i just can't seem to get around it so here it goes ...
Thanks for answering.
You definitely helped me.
I think I am able now to provide my classmates a satisfying explanation for why the levitron levitates.
Im going to search for "simple" information that connects the levitron to the gyroscope and terminate my work.
You were vital to this woks!
Once again, thanks for replying with this precious information.There´s just one thing left that still bothers me...
In my presentation I would like to establish a relationship between the spinning top (Levitron) and a gyroscope. The thing I was looking for as to do with the way they spin...