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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