a triple integral in spherical coordinates to find the volume of the solid bounded by the surface s z=0, z=a, x2+y2+z2= 4a2

a triple integral in spherical coordinates to find the volume of the solid bounded by the surface s z=0, z=a, x2+y2+z2= 4a2

Can u please specify how the boundaries are found and whether its better to integrte it using cylindrical or rectangular coordinates. Thank you in advance

How to find umin(d,r) if xtanθ - (gx^2)/(2u2cos2θ) > r + √(r2-(x-d)2) for d-r < x < d+r ? And 0 < θ < π/2 , d and r can be any positive real number which d &g...

Calculate the work done by the force field F(x,y,z)=(xx +z2 )i + (yy + x2 )j + (zz +y2)k when a particle moves under its influence around the edge of the part of...

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=...

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Derivatives in cartesian, cylindrical, and spherical coordinates, in 3 dimensions and below, with proof.

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...

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...

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...

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...

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 .

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...

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...

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

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

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

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...

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

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?

I do not understand the steps for the Lagrange Multipliers

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