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)). Suppose now that y is regular, and let ø: [−1, 1] → R be a turning angle function for y. Which of the following statements about & are true? Select one or more: O a. The turning angle function is uniquely defined. Ob. There are finitely many possible turning angle functions . There are infinitely many possible turning angle functions p. must have image in [0, π/2]. must have image in [-л/2, 0]. O c. Od. The turning angle function Oe. The turning angle function Of. The turning angle function Og. The turning angle function Oh. For all t in [-1, 1] such that f' (t) = 0, it must be true that sin p(t) can be chosen to have image in [0, π/2]. can be chosen to have image in [-л/2, 0]. Oi. = g' (t) ƒ'(1)* g' (t) For all t in [-1, 1] such that f'(t) = 0, it must be true that (t) = sin 61(0)
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)). Suppose now that y is regular, and let ø: [−1, 1] → R be a turning angle function for y. Which of the following statements about & are true? Select one or more: O a. The turning angle function is uniquely defined. Ob. There are finitely many possible turning angle functions . There are infinitely many possible turning angle functions p. must have image in [0, π/2]. must have image in [-л/2, 0]. O c. Od. The turning angle function Oe. The turning angle function Of. The turning angle function Og. The turning angle function Oh. For all t in [-1, 1] such that f' (t) = 0, it must be true that sin p(t) can be chosen to have image in [0, π/2]. can be chosen to have image in [-л/2, 0]. Oi. = g' (t) ƒ'(1)* g' (t) For all t in [-1, 1] such that f'(t) = 0, it must be true that (t) = sin 61(0)
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)).
Suppose now that y is regular, and let : [-1, 1]
R be a turning angle function for y. Which of the following statements about are true?
Select one or more:
a. The turning angle function is uniquely defined.
Ob. There are finitely many possible turning angle functions.
c. There are infinitely many possible turning angle functions .
must have image in [0, л/2].
must have image in [-л/2, 0].
d. The turning angle function
e. The turning angle function
f. The turning angle function can be chosen to have image in [0, π/2].
g. The turning angle function can be chosen to have image in [-л/2, 0].
Oh. For all t in [−1, 1] such that f'(t) ‡ 0, it must be true that sin (t)
Oi.
=
g' (t)
f'(t).
g' (t)
For all t in [-1, 1] such that f'(t) ‡ 0, it must be true that (t) = sin
f'(t)
For all t in [-1, 1] such that ƒ'(t) ‡ 0, it must be true that cos (t)
k.
For all t in [-1, 1] such that f'(t) ‡ 0, it must be true that (t)
01.
= COS
For all t in [-1, 1] such that ƒ'(t) ‡ 0, it must be true that tan ä(t) =
=
m. For all t in [-1, 1] such that ƒ'(t) ‡ 0, it must be true that (t) =tan(
On. For all t in [−1, 1], it must be true that o' (t) ≥ 0.
Oo. For all t in [−1, 1], it must be true that " (t) ≥ 0.
g' (t)
f'(t)
f'(t)
g' (t)
f'().
g' (t)
' (t)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fe1fc35-672a-49fd-831b-9642c77888ed%2F34a86c7f-14e4-473d-b35e-281b20bdb7dc%2Fk00v8he_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)).
Suppose now that y is regular, and let : [-1, 1]
R be a turning angle function for y. Which of the following statements about are true?
Select one or more:
a. The turning angle function is uniquely defined.
Ob. There are finitely many possible turning angle functions.
c. There are infinitely many possible turning angle functions .
must have image in [0, л/2].
must have image in [-л/2, 0].
d. The turning angle function
e. The turning angle function
f. The turning angle function can be chosen to have image in [0, π/2].
g. The turning angle function can be chosen to have image in [-л/2, 0].
Oh. For all t in [−1, 1] such that f'(t) ‡ 0, it must be true that sin (t)
Oi.
=
g' (t)
f'(t).
g' (t)
For all t in [-1, 1] such that f'(t) ‡ 0, it must be true that (t) = sin
f'(t)
For all t in [-1, 1] such that ƒ'(t) ‡ 0, it must be true that cos (t)
k.
For all t in [-1, 1] such that f'(t) ‡ 0, it must be true that (t)
01.
= COS
For all t in [-1, 1] such that ƒ'(t) ‡ 0, it must be true that tan ä(t) =
=
m. For all t in [-1, 1] such that ƒ'(t) ‡ 0, it must be true that (t) =tan(
On. For all t in [−1, 1], it must be true that o' (t) ≥ 0.
Oo. For all t in [−1, 1], it must be true that " (t) ≥ 0.
g' (t)
f'(t)
f'(t)
g' (t)
f'().
g' (t)
' (t)
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