Homework Statement
Show that n^(logc)/c^(logn) =1 as n->inf where c is a constant greater than 1Homework Equations
The Attempt at a Solution
Tried L'hospitals. But the logs mess it up. Even if you assume that logc>1 then the top does eventually become a constant (second derivative). However...
So i need to prove f0f1 + f1f2...f2n-1f2n=f2n2 where fn is the n-th fibonacci number..
Attempting to solve this i let n=k . Then k=1 and f22=1 which is 1=1 so that is true.
Then i show if the statement is true for k then it is true for k+1, that is f0f1 +...
So i have the equation m*(d2x/dt^2)+c*(dx/dt)+kx=0, where d2x/dt^2 is the second derivative.
So I'm given that m=10 kg, and k=28 N/m. At time t=0 the mass is displaced to x=.18m and then released from rest. I need to derive an expression for the displacement x and the velocity v of the...
14. Suppose there are n=2^k teams in an elimination tournament, where there are n/2 games in the first round, with the n/2=2^(k-1) winners playing in the second round, and so on. Develop a recurrence relation for the number of rounds in the tournament.
So the recurrence relation would be...
http://img708.imageshack.us/img708/8897/symimage.gif [Broken]
so I did x=atanΘ. which is x=3tanΘ and dx is 3sec^2\Theta. Then it is
\sqrt[]{9tan^2\Theta+9}*3sec^2\Theta which evaluates after factoring to \sqrt[]{9sec^2\Theta}*3sec^2\Theta which is then 3sec\Theta*3sec^2\Theta If i take...
An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find the work needed
to pump half the water out of the aquarium. (The density of water, p, is 1000 kg/m3,
and acceleration due to gravity, g, is 9.8 m/s2.)
So in order to truly understand how to do these kind of problems I decided...
The terminal side of an angle theta in standard position passes through (-2,-3). What is sec theta?
How would you solve this problem without a calculator?
Thanks.
I have heard that there have been research done with a controlled experiment that the answers the ouija board gives back is not always random letters. Do you have a site or something for this?