Find the following: f(x, y, z) = e^(xy) sin z j + y tan^−1(x/z)k exercise find the curl and the divergence of the vector field.

Divergence is easier to compute:

Curl is a bit more tedious. Denote by the differential operator, namely the derivative with respect to the variable . Then

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g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)