The problem reads: "Consider a particle moving through space along the trajectory r(t) = (cos(t),sin(t),t) for t≥0. Draw a nice picture of this trajectory. Suppose that at time t0=...

The problem reads: "Consider a particle moving through space along the trajectory r(t) = (cos(t),sin(t),t) for t≥0. Draw a nice picture of this trajectory. Suppose that at time t0=...

How would I write this in matrix form (x' = AX) x' = x y' = y Note: Is it supposed to be like this: x' = (1 v 1)(x v y) or x' = (1 + 0 v 1 + 0)(x v...

a. Suppose ƒ is continuous and a > 0. Show that ∫0a ∫0y ∫0z ƒ(x) dx dz dy = (1/2) ∫0a (a-x2) ƒ(x) dx. b...

Let exyz = 2. Find zx and zy in 3 ways and check for agreement. a. use result of a previous exercise (i.e. Assume that F(x,y,z(x,y))=0 implicitly defines z as a differentiable...

Find the four second partial derivatives. Observe that the second mixed partials are equal. z = 4 ln(x − y)

Find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously. f(x, y) = x2 + 4xy + y2 − 34x − 32y + 38

and i would like steps if possible to help explain how you got the answer

The function F(x,y) is deﬁned by F(x,y) =∫xx/y e-(t^2) dt Find Fx,Fy and verify that (∂Fx)/∂y = (∂Fy)/∂x .

f(x, y)= x2+4xy-y2; P(2,1) a. find unit vectors that give direction of steepest ascent and steepest descent at P. b. find a vector that points in a direction of no...

f is function of a single variable; assume it is at least twice differentiable. Let z = g(x,y) be a function of x and y and let u = u(z) = f(g(x,y)). Establish the following...

A mountain having an elliptical base can be described by the equation z = 25−x2 −4y2. A climber will try to reach the top starting at the point of coordinates (3,2,0). The climber wants to be always...

For f(x, y), find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously. f(x, y) = 36 x + 6 y + xy

Consider the initial value problem: dy/dx=y^2 + 5y − 6, y(X0) = (Y0) (a) Verify that the hypotheses of the existence and uniqueness theorem are satisfied. (b) Suppose that...

I do not understand the steps for the Lagrange Multipliers

Show that f(z)=[sin(PI/z)]/(z+2) is nowhere analytic for |z|<a , where a is a some positive number. Can you help me to solve this problem?

Evaluate the triple integral of x^2 where D is the region inside the cylinder x^2+y^2=9 which is bounded below by the plane z=0 and bounded above by the plane 4x+4y+z=19 I...

More specifically, what geometrical properties does a function need to have, in order to satisfy the laplace equations? (other than it being 2nd order differentiable)

Consider the curve C given by the equation: C · · · √ x + √ y = √ a, where a is a constant, a > 0. Let (x0, y0) with x0 > 0, y0 > 0, be a point on C. If (x1, 0) and (0, y1) are x...

Evaluate the double integral D of 3/(4 +y^3) where D= {(x,y) | 0 <x <1, x^(1/2) <y <1}

Full working out please