Question

Find div v and its value at P
v=[0, cos x y z, sin x y z], P:(2, π/2, 0)

Answer 1

To find div v, calculate the partial derivatives of each component of v with respect to x, y, and z, then add them together. Substitute the given values into the derivatives to find the value of div v at a specific point.

Step-by-step explanation:

To find div v, we need to calculate the partial derivatives of each component of v with respect to their corresponding variables x, y, and z and then add these derivatives together.

Div v = ∂/∂x (0) + ∂/∂y (cos(xy)) + ∂/∂z (sin(xy))

Using the given value P:(2, π/2, 0), we substitute these values into the partial derivatives and evaluate to find the value of div v at P.

Div v = (∂/∂x (0) at P) + (∂/∂y (cos(xy)) at P) + (∂/∂z (sin(xy)) at P)