Having a melt down as I have done this problem twice now and my exam is tomorrow and I can't seem to figure it out anymore.... ugh.
1. Homework Statement
The depth of a lake at the point on the surface with coordinates (x, y ) is given by D(x, y ) = 100−4x 2 −y 2 . a) If a boat at the point...
I have a few conceptual questions that I'd like to clear up if possible.
The first is about directional derivatives in general. If one has a function f defined in some region and one wishes to know the rate of change of that function (i.e. its derivative) along a particular direction in that...
1.
Given a function f(x,y) at (x0,y0). Find the two angles the directional derivative makes with the x-axis, where the directional derivative is 1. The angles lie in (-pi,pi].
2.
f(x,y) = sec(pi/14)*sqrt(x^2 + y^2)
p0 = (6,6)
3.
I use the relation D_u = grad(f) * u, where u is the...
I understand that a tangent vector, tangent to some point p on some n-dimensional manifold \mathcal{M} can defined in terms of an equivalence class of curves [\gamma] (where the curves are defined as \gamma: (a,b)\rightarrow U\subset\mathcal{M}, passing through said point, such that \gamma (0)=...
Recently I started with multivariable calculus; where I have seen concepts like multivariable function, partial derivative, and so on. A week ago we saw the following concept: directional derivative. Ok, I know the math behind this as well as the way to compute the directional derivative through...