Chapter 14: Q. 25 (page 1096)
Sketch the vector fields in Exercises 25–32.
Short Answer
Sketch of the vector fields is

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Chapter 14: Q. 25 (page 1096)
Sketch the vector fields in Exercises 25–32.
Sketch of the vector fields is

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Give a smooth parametrization of the upper half of the unit sphere in terms of x and y.
Given a smooth surface S described as a function z = f(x, y), calculate the upwards-pointing normal vector for S.
Integrate the given function over the accompanying surface in Exercises 27–34.
, where S is the portion of the paraboloid that lies above the rectangle determined by and in the xyplane.
If S is parametrized by r(u, v), why is the correct factor to use to account for distortion of area?
Why is in Green’s Theorem replaced by in Stokes’ Theorem?
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