MATH 21D Final Exam Fall 2004
T/F: Label the following statements in the space provided. Use the label
T is the statement is true and the label F if the statement is false. (No
explanation required. Each correct label is worth two points.)
The unit sphere is an orientable surface.
If Fis defined on a region including Sand C1and C2are two boundary
components of the surface S, then RC1F·dris necessarily equal to RC2F·dr.
If the unit circle is oriented counterclockwise and the upper hemisphere
of the unit sphere is oriented via the right hand rule, then the normal vector
npoints away from the origin.
j×k=i.
The vector A×Bis perpendicular to both Aand B.
The directional derivative of a function fin a direction perpendicular
to the gradient is necessarily 0.
The tangent plane of the graph of the function z=f(x, y) at the point
(a, b, f (a, b)) is necessarily normal to 5f.
If curl F =0, then Fis necessarily conservative.
||∇f(x0, y0, z0))|| is the maximum directional derivative of fat (x0, y0, z0).
The surface area of a sphere of radius ris 4πr2.
The Moebius band (see page 3) is simply connected.
The unit disk in the xy-plane is simply connected.
The Moebius band (see page 3) is orientable.
The tangent plane to the graph of the function z=f(x, y) at the point
(a, b, c) necessarily meets all points (x, y, f (x, y)).
If Fis conservative, then Fis necessarily 0.
If two rows of a matrix are identical, then the determinant of the
matrix is necessarily 0.
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