We just started Multivariable at school after AP and I have a problem set to do. Since, I am newbie, so I am struggling a bit.
1. Suppose the current I in an electrical circuit is related to voltage V and the resistance R by the equation I=V/R. If voltage drops from 24 to 23 volts and resistance drops from 100 ohms to 80 ohms, will I increase or decrease by how much ?
2. Find the derivation of f(x,y,z)=xyz in the direction of the velocity vector of the helix r(t)=cos3t i + sin3t j + 3t k at t=pi/3
3. At the point (1,2) the function f(x,y) has a derivative of 2 in the direction toward (2,2) and derivative of -2 in the direction toward (1,1)
a. Find D1f(1,2) and D2f(1,2)
b. Find the derivative of f at (1,2) in the direction toward (4,6)
The Attempt at a Solution
1. So I took the partial derivative and got D1f= 1/R and D2f= -V/R^2.
2. So I found the gradient vector for f as yz i + xz j + xy k
I also found r(pi/3)= -1 i + pi k
How do I find the value of x,y,z and also, do I need to find the unit vector of r ?
So for delta I = 1/R*delta V - V/R^2*delta R. Plugging in the numbers I got a decrease but it should be an increase. Where did I do wrong ?
3. Any suggestion on how to do this problem ??