oh...I get it,, thanks for the graph. I completely misunderstood the definition of diverge and converge. I thought that converging meant that the function approached a finite limit as x approached infinity, because when learning about infinite integrals, we also talked about convergence and...
about the radius of convergence...when i'm calculating, i understand that i can get a solution algebraically, but sometimes i wonder what it would look like on a graph, because I just can't seem to imagine how there would be a boundary to convergence.
would I be right to assume it behaves like...
Homework Statement
I read that the taylor series was a way to approximate the a function f(x) graphically, by addition and subtraction.
So say I have \frac{1}{1-x}=1+x+x^{2}+x^{3}+...+x^{n}...
suppose x=3, then the left and right side of the equation can't possibly equal the same thing...
Wow...that first method was sure tedious...I'm glad you suggested symmetry before I did the problem.
so...in this question, the total resistance is 1 ohm...I think...yeah.
This is a cool way of looking at circuits, thanks so much for helping me clear up the confusion!
Hey! this suddenly makes a whole lot of sense! So...I gave another shot at the problem, and I got \frac{5}{6}ohms. would that be closer to the answer?
and so...if i have two points in the circuit at the same potential, I'd be able to connect the nodes, or take away the branch inbeween, without...
Derivatives of inverse functions--how two formulas relate?
Homework Statement
I know two formulas for calculating the derivative of an inverse function, both of which I know how to derive, but I don't know how to relate them to one another.
Homework Equations...
Well, what I'm trying to do...is actually what i couldn't wrap my head around in my former question "Kirchoff's Loop Rule--Direction of Current?", which you helped me answer for the most part, thank you very much.
however, i still have a slight problem, and I posted it on the other question...
I suppose it wouldn't change anything...right?
but in a way...if, "there isn't anything 'pushing' the current down the wire", then the wire might as well not be there at all. So...instead of colapsing the nodes together, wouldn't taking the branch out entirely be another option?
Of course, if...
While doing some questions using Kirchhoff's laws, I came across this problem, as shown in the picture.
Obviously, no current passes through the 5 ohm resistor. But then I get confused.
1) If "no current" passed through the branch, wouldn't that be as if the branch weren't there? that would...
haha, did you just quote the answer key? That was exactly what I got from the explanation, and exactly what I didn't understand. the circuit does have symmetry, but...I'm thinking, that after the current passes through the top left resistor, it faces two equal paths...so the current may as well...
so, when the current from the 10ohm resister on the left first, it's more likely to go towards the second 10 ohm easier path, but when current goes from the 20ohm resistor on the top right, won't a small portion of current still have to go down to the 20 ohm resistor on the bottom right? So why...
Kirchoff's Loop Rule--Direction of Current?
I came across this question, and it really confused me-- how does the current decide which direction it goes?
The pictures are attatched below.
The first picture is of the original questions. It gives two scenarios, and asks you what the value...
my apologies, I thought i did upload the picture.
But you got the gist of the problem from the without the picture anyways.
Unit check, the fundamental approach to going over problems---why didn't I think of that?
I do understand the cosθ, thx for asking
Thank you for taking the time to...
so, what would be another example of "infinite" density?
why would a surface charge distribution not have "finite" density? is it because that a surface has no volume?
Homework Statement
"as long as the volume charge density is finite (which is not true of surface charge distributions or point charges), the electric field is continuous.
Homework Equations
The Attempt at a Solution
I know that for surface charges distributions and point charges...
calculating electric fields due to continuous charge distributions?
a question I came across doing some electric field questions, and the answer was really confusing.
Homework Statement
Charge is distributed along a linear semicircular rod with a linear charge density λ as in picture...
Homework Statement
A mass m hanging on a spring oscillates vertically. If the equilibrium point of the oscillation is a distance d below the relaxed length of the spring and if the amplitude of the oscillation is A, what is the maximum kinetic energy of the oscillation?
[b]2. Homework...
this is another conceptual question, so sorry for not following the template.
I thought that angular frequency and angular velocity shouldn't be the same thing, but after going through some of the forum threads, there was the idea: "the only difference between angular frequency and angular...
bingo.
I think i get it a lot better now.
one last question---
if an object was rolling without slipping at constant speed on a surface with friction, it wouldn't experience any friction at all, but this situation isn't possible, because as long as an object is rolling on a surface with...
ok, I get this, thank you.
so even on a surface with friction, as long as the object is rolling without slipping at a constant speed, there is no friction between the object and the surface, because there is no relative motion at the point of contact?
wait. but at the point of contact...
yes, there is no relative motion between the object and the surface, but wouldn't there be static friction, or at least some sort of external torque to keep the object spinning?
or maybe you're right, i can understand that no relative motion means no friction, but then how would we use friction...
sorry, this is is a general question about a conceptual definition I read in my textbook, i hope that's ok.
"an object that rolls without slipping at a constant velocity over a surface with friction experiences no frictional force"
is this true?
i understand that on a frictionless surface, the...