As in the previous question, let f, g: [-1, 1] → R be smooth strictly increasing functions, and define a smooth curve y: [-1, 1] → R² by y(t) = (f(t), g(t)). Assume now that y is regular, and let K, be the total signed curvature of gamma. What is the maximum possible value of Ks? Select one: O a. 一元 O b. -2 O с. -π/2 O d. -1 O е. -π/4 O f. -1/2 Og. 0 O h. 1/2 Oi. π/4 Oj. 1 Ok. π/2 O I. O 2 m. π n. K, can take arbitrarily large values, but if y is unit speed then we must have K, ≤ π. Oo. K, can take arbitrarily large values, even if y is unit speed, so there is no maximum. Op. None of the above.
As in the previous question, let f, g: [-1, 1] → R be smooth strictly increasing functions, and define a smooth curve y: [-1, 1] → R² by y(t) = (f(t), g(t)). Assume now that y is regular, and let K, be the total signed curvature of gamma. What is the maximum possible value of Ks? Select one: O a. 一元 O b. -2 O с. -π/2 O d. -1 O е. -π/4 O f. -1/2 Og. 0 O h. 1/2 Oi. π/4 Oj. 1 Ok. π/2 O I. O 2 m. π n. K, can take arbitrarily large values, but if y is unit speed then we must have K, ≤ π. Oo. K, can take arbitrarily large values, even if y is unit speed, so there is no maximum. Op. None of the above.
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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![As in the previous question, let ƒ, g: [−1, 1] → R be smooth strictly increasing functions, and define a smooth curve y: [−1, 1] → R² by
y(t) = (f(t), g(t)).
Assume now that y is regular, and let K, be the total signed curvature of gamma. What is the maximum possible value of Ks?
Select one:
O a. -T
O b. -2
O c. -π/2
d. -1
е. -π/4
- 1/2
O f.
g. 0
Oh. 1/2
O i.
л/4
1
O j.
Ο κ. π/2
OI. 2
O
m. π
n. K, can take arbitrarily large values, but if y is unit speed then we must have K, ≤ л.
Oo. K, can take arbitrarily large values, even if y is unit speed, so there is no maximum.
p. None of the above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fe1fc35-672a-49fd-831b-9642c77888ed%2Ff10c63f1-c86d-485e-a850-eb3029fe9ee5%2Fjmbgmq4_processed.png&w=3840&q=75)
Transcribed Image Text:As in the previous question, let ƒ, g: [−1, 1] → R be smooth strictly increasing functions, and define a smooth curve y: [−1, 1] → R² by
y(t) = (f(t), g(t)).
Assume now that y is regular, and let K, be the total signed curvature of gamma. What is the maximum possible value of Ks?
Select one:
O a. -T
O b. -2
O c. -π/2
d. -1
е. -π/4
- 1/2
O f.
g. 0
Oh. 1/2
O i.
л/4
1
O j.
Ο κ. π/2
OI. 2
O
m. π
n. K, can take arbitrarily large values, but if y is unit speed then we must have K, ≤ л.
Oo. K, can take arbitrarily large values, even if y is unit speed, so there is no maximum.
p. None of the above.
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