For each point (x, y, z) on a surface S, let n(x, y, z) be a...

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For each point (x, y, z) on a surface S, let n(x, y, z) be a unit normal vector to S at (x, y, z). The so called normal derivative of a differentiable function f: R³ R is the directional derivative Dnf of f in the direction of n. (a) For a positive parameter a, let S denote the portion of the sphere x² + y² +2²=a² in the first octant (i.e., where a ≥ 0, y 20 and z 20), oriented by the unit normal vector that points away from the origin. Let f(x, y, z) = ln (x² + y² +2²). Evaluate S Dnf ds. For each point (x, y, z) on a surface S, let n(x, y, z) be a unit normal vector to S at (x, y, z). The so called normal derivative of a differentiable function f: R³ R is the directional derivative Dnf of f in the direction of n. (a) For a positive parameter a, let S denote the portion of the sphere x² + y² +2²=a² in the first octant (i.e., where a ≥ 0, y 20 and z 20), oriented by the unit normal vector that points away from the origin. Let f(x, y, z) = ln (x² + y² +2²). Evaluate S Dnf ds.

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To evaluate the normal derivative of the function fx y z lnx y 22 on the surface S we need to calcul... View the full answer