Recall that the Laplacian of a function f : R3 → R is defined by ∆f = div(∇f). (a) Prove that ∆(fg) = f∆g + g∆f + 2∇f · ∇g.
(b) Show that div(f∇g − g∇f) = f∆g − g∆f.

Given the parent function of [tex]f(x)=x^4[/tex], what change will occur when the function is changed to [tex]f(\frac{1}{2} x)[/tex]?

Acircle has a circumference of 28.36 units what is the diameter of the circle

Someone answer asap for ! michele pushes a box d meters across a floor. she uses a force f, in newtons, to push the box. she pushes the box for t seconds. the formula p = fd/t calculates the power, p, in watts, that it takes for michele to complete the task. solve the formula for d.