o(u, v) = (u sin(u) cosh(v), 1- cos(u) cosh(v), -4 sin where o is defined on a sufficiently small open set UC R² to be a regular surface patch, with image S. Is S a minimal surface? Indicate yes or no, along with the best reasoning from the choices below. Select one: O a. Yes, as one of its principal curvatures is zero at the origin. O b. Yes, as one of its principal curvatures is always zero. O c. Yes as both of its principal curvatures are zero at the origin. O d. Yes, as both of its principal curvatures are always zero. (2) sinh(;)),
o(u, v) = (u sin(u) cosh(v), 1- cos(u) cosh(v), -4 sin where o is defined on a sufficiently small open set UC R² to be a regular surface patch, with image S. Is S a minimal surface? Indicate yes or no, along with the best reasoning from the choices below. Select one: O a. Yes, as one of its principal curvatures is zero at the origin. O b. Yes, as one of its principal curvatures is always zero. O c. Yes as both of its principal curvatures are zero at the origin. O d. Yes, as both of its principal curvatures are always zero. (2) sinh(;)),
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:As in the previous question, let
where o is defined on a sufficiently small open set UC R² to be a regular surface patch, with image S.
Is S a minimal surface?
Indicate yes or no, along with the best reasoning from the choices below.
Select one:
a.
Yes, as one of its principal curvatures is zero at the origin.
O b.
Yes, as one of its principal curvatures is always zero.
O c.
Yes as both of its principal curvatures are zero at the origin.
O d. Yes, as both of its principal curvatures are always zero.
Yes, as its Gaussian curvature is zero at the origin.
Yes, as its Gaussian curvature is always zero.
g.
Yes, as its mean curvature is zero at the origin.
Oh. Yes, as its mean curvature is always zero.
O i.
O j.
Ok.
O I.
u
o(u, v) = (u – sin(u) cosh(v), 1 − cos(u) cosh(u), –4 sin(
e.
O f.
No, as one of its principal curvatures is nonzero at the origin.
No, as one of its principal curvatures is always nonzero.
No, as both of its principal curvatures are nonzero at the origin.
No, as both of its principal curvatures are always nonzero.
m.
No, as its Gaussian curvature is nonzero at the origin.
n. No, as its Gaussian curvature is not always zero.
o. No, as its mean curvature is nonzero at the origin.
p. No, as its mean curvature is not always zero.
h(²-)),
sinh
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