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## Calculus 3 Answers

Use Lagrange multipliers to find the maximum and minimum values

Use Lagrange multipliers to find the maximum and minimum values

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...

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=...

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...

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...

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...