Show that (a, b) is open and [a, b] is closed; First, recall the definition of an open set: UCR is open, if for every xo EU, there is € > 0, such that D (xo, e) ≤U. Please consider the following steps: We show that (a, b) is open. • Let xo € (a, b), then xo − a > 0 and b - xo > 0. • Define € = • Show that D (xo, €) ≤ (a, b) by taking x € D (xo, e) and showing that x = (a, b). You may need to use 0 < € ≤ xo - a and 0 < € ≤ b - xo in your argument. Recall the definition of a closed set: FCR is closed if Fc = R\F is open Please consider the following steps: We show that [a, b]° = R\ [a, b] = (-∞, a) U (b, ∞) is open. • Take xo € [a, b], then xo b. Therefore, a - xo > 0 and xo - b>0. • Define € = • Show that D (xo, €) ≤ (-∞, a) U (b, ∞) by taking x € D (xo, €) and showing that x = (-∞, a) U (b, ∞).
Show that (a, b) is open and [a, b] is closed; First, recall the definition of an open set: UCR is open, if for every xo EU, there is € > 0, such that D (xo, e) ≤U. Please consider the following steps: We show that (a, b) is open. • Let xo € (a, b), then xo − a > 0 and b - xo > 0. • Define € = • Show that D (xo, €) ≤ (a, b) by taking x € D (xo, e) and showing that x = (a, b). You may need to use 0 < € ≤ xo - a and 0 < € ≤ b - xo in your argument. Recall the definition of a closed set: FCR is closed if Fc = R\F is open Please consider the following steps: We show that [a, b]° = R\ [a, b] = (-∞, a) U (b, ∞) is open. • Take xo € [a, b], then xo b. Therefore, a - xo > 0 and xo - b>0. • Define € = • Show that D (xo, €) ≤ (-∞, a) U (b, ∞) by taking x € D (xo, €) and showing that x = (-∞, a) U (b, ∞).
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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Please follow the instructions given in the question thanks.
![Show that
(a, b) is open and [a, b] is closed;
First, recall the definition of an open set: UCR is open, if for every xo EU, there is € > 0, such
that D (xo, e) ≤U.
Please consider the following steps: We show that (a, b) is open.
• Let xo € (a, b), then xo − a > 0 and b - xo > 0.
• Define € =
• Show that D (xo, €) ≤ (a, b) by taking x € D (xo, e) and showing that x = (a, b).
You may need to use 0 < € ≤ xo - a and 0 < € ≤ b - xo in your argument.
Recall the definition of a closed set: FCR is closed if Fe = R\F is open
Please consider the following steps: We show that [a, b]° = R\ [a, b] = (-∞, a) U (b, ∞) is open.
• Take xo € [a, b], then xo <a or xo> b. Therefore, a - xo > 0 and xo - b>0.
• Define € =
• Show that D (xo, €) ≤ (-∞, a) U (b, ∞) by taking x € D (xo, €) and showing that x = (-∞, a) U
(b, ∞).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8d46346-fe9f-45aa-a3a0-df12b7cae379%2F2d63f99f-b20b-4235-9543-692181421e60%2Fh9di29x_processed.png&w=3840&q=75)
Transcribed Image Text:Show that
(a, b) is open and [a, b] is closed;
First, recall the definition of an open set: UCR is open, if for every xo EU, there is € > 0, such
that D (xo, e) ≤U.
Please consider the following steps: We show that (a, b) is open.
• Let xo € (a, b), then xo − a > 0 and b - xo > 0.
• Define € =
• Show that D (xo, €) ≤ (a, b) by taking x € D (xo, e) and showing that x = (a, b).
You may need to use 0 < € ≤ xo - a and 0 < € ≤ b - xo in your argument.
Recall the definition of a closed set: FCR is closed if Fe = R\F is open
Please consider the following steps: We show that [a, b]° = R\ [a, b] = (-∞, a) U (b, ∞) is open.
• Take xo € [a, b], then xo <a or xo> b. Therefore, a - xo > 0 and xo - b>0.
• Define € =
• Show that D (xo, €) ≤ (-∞, a) U (b, ∞) by taking x € D (xo, €) and showing that x = (-∞, a) U
(b, ∞).
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