2. Let ao E R be an initial point. For each n > 0, we define Зал if an < 0.5, - 3a, +3 if an > 0.5. (a) Prove that if ao < 0 or ao > 1, then lim, y an = -00. (b) Let ao be an arbitrary point in the Cantor set. For each n > 1, determine whether or not a, belongs to the Cantor set. Justify your answer. [Hint: Use the ternary representation of a point in the Cantor set.]
2. Let ao E R be an initial point. For each n > 0, we define Зал if an < 0.5, - 3a, +3 if an > 0.5. (a) Prove that if ao < 0 or ao > 1, then lim, y an = -00. (b) Let ao be an arbitrary point in the Cantor set. For each n > 1, determine whether or not a, belongs to the Cantor set. Justify your answer. [Hint: Use the ternary representation of a point in the Cantor set.]
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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a,b please
![2. Let ao E R be an initial point. For each n > 0, we define
3an
if an < 0.5,
- 3a, +3 if an > 0.5.
(a) Prove that if ao < 0 or ao > 1, then lim,, y∞ an =
(b) Let ao be an arbitrary point in the Cantor set. For each n > 1, determine whether
or not a„ belongs to the Cantor set. Justify your answer. [Hint: Use the ternary
representation of a point in the Cantor set.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1af2e839-a835-4130-9203-42e58df89277%2F0e424006-cb71-4e5f-b124-09c1b3b2a842%2Fipwz8xo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Let ao E R be an initial point. For each n > 0, we define
3an
if an < 0.5,
- 3a, +3 if an > 0.5.
(a) Prove that if ao < 0 or ao > 1, then lim,, y∞ an =
(b) Let ao be an arbitrary point in the Cantor set. For each n > 1, determine whether
or not a„ belongs to the Cantor set. Justify your answer. [Hint: Use the ternary
representation of a point in the Cantor set.]
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