# rapidly

1. ### Converges Rapidly to Square Root of A??

,.,good day evryone,.i need ur help with this,.how should i prove this?? If A>0 and X1>0, the sequence defined by the attachment converges rapidly to squareroot of A
2. ### Rapidly decreasing functions and convergence

I am trying to show that, for f a rapidly decreasing function, the mapping from f to f' is continuous. Since the space of RDF's is an F-space, Rudin says that I can use the closed graph theorem for F-spaces, and hence I need to show that the graph of the mapping is closed. So I wish to show...
3. ### Changing least rapidly?

At (2,1), I have to find the direction where f(x,y)=x^2+3xy-y^2 is increasing fastest. So I did: \triangledown f(2,1)= \langle 2(2)+3, 3(2)-2 \rangle = \langle 7,4 \rangle Next I have to find the rate of growth in this direction, so I did: ||\triangledown f(2,1)|| = \sqrt{7^2+4^2} =...
4. ### f decreases most rapidly at Q

Find a unit vector in the direction in which f decreases most rapidly at Q Thank u!
5. ### Show that a differentiable function f decreases most rapidly....

at x in the direction opposite to the gradient vector, that is, in the direction of -Vf(x). I made up a function of two variables f(x, y) = ln(x^2 -y^3/2) and then calculated the gradient which came to 2x/(x^2 - y^3/2) and -3/2y^2/(x^2 - y^3/2). I then put in a value Vf (2, 1) and got the...
6. ### Depth of water when the water level is falling the least rapidly

Can someone help me with this problem? Thank you. A spherical tank of radius 10ft is being filled with water. When it is completely full, a plug at its bottom is removed. According to Torricelli's law, the water drains in such a way that dV/dt = -k*sqrt(y), where V is the volume of water in the...