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...