Homework Statement
Find the extrema of f(x, y) = x2−2xy+ 2y2, subject to the
constraint x2 +y2 = 1.Homework Equations
∇f(x,y) = λg(x,y)The Attempt at a Solution
This is the work I have thus far:
Letting g(x,y) = x2+y2-1,
We obtain the following three equations from the Lagrange Multiplier...
Well, as I said, if \dot{\vec{L}} = 0, then the net torque and net force are zero. The constant velocity magnitude implies that the direction of the velocity vector can change but the speed would remain constant.
If F is zero, then you have
m\ddot{x} = 0
Which implies that x(t) is of...
Homework Statement
Determine possible trajectories for particle with constant magnitude of velocity |\dot{\vec{r}}| = v0 and constant angular momentum \vec{L} = \vec{L}0
Homework Equations
|\dot{\vec{r}}| = v0
\vec{L} = \vec{L}0The Attempt at a Solution
I know that L dot is zero and...
To be more specific, I am supposed to approximate this number using linearization and differentials i.e
i) L(x) ≈ f(a)+\frac{df(a)}{dx}(x-a) when f(x) ≈ L(x) only when x is close to a
ii) f(a+dx)≈f(a)+dy where dy=\frac{df(x)}{dx}dx
Homework Statement
The goal is to approximate the number \frac{-1+\sqrt{5}}{2} using linearization methods.
Homework Equations
This number is a solution to x^{2}=1-x
The Attempt at a Solution
I was told to use f(x)= x^{2}+x-1 with the Newton method to find x_{1},x_{2},x_{3},x_{4} at...