The Directional Derivative and the Rate of Change: When calculating the directional derivative of a function, we are obtaining the rate of change of a function since it is related to the gradient of the function and the gradient of the function is composed of the partial derivatives.

Answer to: Find the rate of change of f(x, y, z) = xyz in the direction normal to the surface yx^2 + xy^2 + yz^2 = 75 at (1, 5, 3).

mean and variance: Mean is defined as the weighted average of the possible values that the random variable can take.

Stokes theorem:: The line integral of the tangential component of a finite and differentiable vector around a simple closed curve C is equal to the surface integral of the outward unit normal component of a curl of the vector function over any surface S having as its boundary.

Find the mass, the center of mass and the moment of inertia about the x-axis of a thin plate bounded by the parabola x=y-y^2 \ and \ the \ line \ x+y=0 \ if \ the \ density \ is \ \delta \ (x,y)=x+y

(a) Calculate the moment of inertia of a solid cylinder of mass 4.21 kg and radius 8.9 m about an axis parallel to the center-of-mass axis and passing through the edge of the cylinder.

Use Stokes' theorem to evaluate integral over C of F dot dr when F = (x, y, x^2 + y^2) and C is the boundary of z = 1 - x^2 - y^2 in the first octant.

List the points in the {eq}xy {/eq}-plane, if any, at which the function {eq}z = e^{\frac{-y}{x^2+y^2}} {/eq} is not differentiable.

Using only your brain, draw a contour map for the function {eq}z = f(x, y) = \frac{y}{x^2 + 1}. {/eq} Show level curves for z-levels of {eq}-2, -1, -\frac{1}{2}, 0 ...

Answer to: What is the general solution to frac{dy}{dx} = frac{2y^3 + yx^2 - 2x^3}{2y^2x}? By signing up, you'll get thousands of step-by-step...