Recent content by dba

Homework Statement I try to order given functions and I am stuck with evaluating the following: f(n)= (n+1)! and g(n)=n^{logn} Homework Equations \lim_{n\to\infty}\frac{f(n)}{g(n)} = 0 then g(n) is faster growing. \lim_{n\to\infty}\frac{f(n)}{g(n)} = \infty then f(n) is...

Thank you very much. I understand this now :smile:

Homework Statement I have trouble with the summation notation. \sum_{i=0}^{k}\binom{k}{i}f_{n+i} How do I write this as a sequence based on the definition of Fibonacci sequence? Homework Equations Definition: f(0)=0 f(1)=1 f(n)=f(n-1) + f(n-2) for n>=2 Example: f(2) = f(1) +...

Yes, I see it. i did write is good on my paper. soory about that. How would I express a referal to the first part with f and g reversed. Something like: since f(n)=O(g(n)) implies that g(n)=Ω(f(n)) we can say that g(n)=O(f(n)) implies that f(n)=Ω(g(n)) ? Thank you very much for your help!

Is this proof correct? f(n)=O(g(n)) \Leftrightarrow g(n)=Ω(f(n)) LHS → f(n)=O(g(n))→ f(n) ≤ c*g(n) → (1/c)*f(n) ≤ g(n) → g(n) ≥ (1/c)f(n) where d=1/c → g(n) = Ω(g(n)) → RHS RHS → g(n)= Ω (f(n))→ g(n) ≥ d*f(n) →(1/d)*g(n) ≥ f(n) → f(n) ≤ (1/d)g(n) where c=1/d → f(n) = O (f(n)) → LHS...

Thank you. Your explanation makes it much easier to understand. I will try to proof what you said and see what I get. :-)

mmmh. Ok the problem states: prove that the notation is symmetric: for any function f,g,h:N→R>=0 if f(n)=θ(g(n)) then g(n) = θ(f(n)) So, I looked at the definition of Big Theta which is if d*f(n) <= t(n) <= c*f(n) then t(n)=θ(f(n)) Thus, both conditions need to be true: t(n) <=...

Homework Statement proof if f(n) = O(g(n)) then g(n) = O(f(n)) = stands for element of c is some constant Homework Equations if f(n) <= c*g(n) then f(n) = O(g(n)) if g(n) <= c*f(n) then g(n) = O(f(n)) The Attempt at a Solution I tried to go from the left-hand-side(LHS) to the...

Homework Statement Reduce, x(w+y'+z') + (w+x)y'z + wx'yz + wxy Homework Equations + stands for OR * (multiplication) stands for AND ' NOT The Attempt at a Solution I tried to combine some terms but I cannot find a good start... x(w+y'+z') + (w+x)y'z + wx'yz + wxy = xw + xy'+...

Homework Statement I need to simplify the boolean expression by algebraic manipulation as much as possible. (a+b+c)*(a'+c)*(a'+b') Homework Equations + stands for OR * stands for AND (or no operator between variables) ' Stands for NOT The Attempt at a Solution I tried but I do not...

That is exactly what I do not understand. I do not know how to imagine a direction of a change. As I mentioned in the beginning, I would assume if my B goes to zero, then the flus will be zero and the current will be zero. therefore there would't be a direction.

Can you explain a little better what you mean by the direction of the change in the flux? For the problem, there are no numbers. There is a vertical loop and the direction of the field is to the right. The flux is the integral of B*A since B and da are parallel and A is pi*r^2. Thanks!.

Homework Statement In our lab about transformers we have a question as follows: Consider a loop in a uniform magnetic field. If the field is suddenly turned off, in which direction will the current flow in the wire? Homework Equations The Attempt at a Solution My first thought...

Thank you so much for your help!

Any potential from 0 to 0.72 Volt which is smaller than the voltage of the battery of 1.5 Volt. And Vab has to be equal to the battery voltage to allow the current to be zero. Is that correct? is that the reason why I could not find the null current?