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I need answer question 1.2.6 number (b) to find limit only ? and i need answer 1.2.7 (a) and (b) to find limit only.

I need answer question 1.2.6 number (b) to find limit only ? and i need answer 1.2.7 (a) and (b) to find limit only.

Advanced Engineering Mathematics
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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I need answer question 1.2.6 number (b) to find limit only ? and i need answer 1.2.7 (a) and (b) to find limit only.

AA E 1.2.6. Show that the following sequences of sets, {Ck}, are nondecreasing, (1.2.16) O, then find limco Cr. a. Cr = {x: 1/k <e< 3-1/k}, k = 1, 2, 3, .... b. Ck = {(x, y) : 1/k < a² + y? < 4 – 1/k}, k = 1,2, 3, .... |3D 1.2.7. Show that the following sequences of sets, {Ck}, are nonincreasing, (1.2.17) O, then find lim, 0Ck. a. C = {x: 2-1/k < x <2}, k = 1, 2, 3, .... b. C = {x : 2 < ¤ < 2 + 1/k}, k = 1, 2, 3, . %3D .... c. C = {(x, y) : 0 <a² + y? < 1/k}, k = 1, 2, 3, . %3D .... 1.2.8. For every one-dimensional set C, define the function Q(C) = Ecf(x), where f (x) = ())',x = 0, 1, 2, . zero elsewhere. If C1 = {x : x = 0, 1, 2, 3} and C2 = {x : x = 0, 1, 2, ...}, find Q (C1) and Q(C2). %3D Hint: Recall that Sn = a+ ar + + ar"-1 = a (1- r")/(1 – r) and, hence, it follows that lim,00 Sn = a/ (1 - r) provided that Ir| < 1. !! ... 10
Transcribed Image Text:AA E 1.2.6. Show that the following sequences of sets, {Ck}, are nondecreasing, (1.2.16) O, then find limco Cr. a. Cr = {x: 1/k <e< 3-1/k}, k = 1, 2, 3, .... b. Ck = {(x, y) : 1/k < a² + y? < 4 – 1/k}, k = 1,2, 3, .... |3D 1.2.7. Show that the following sequences of sets, {Ck}, are nonincreasing, (1.2.17) O, then find lim, 0Ck. a. C = {x: 2-1/k < x <2}, k = 1, 2, 3, .... b. C = {x : 2 < ¤ < 2 + 1/k}, k = 1, 2, 3, . %3D .... c. C = {(x, y) : 0 <a² + y? < 1/k}, k = 1, 2, 3, . %3D .... 1.2.8. For every one-dimensional set C, define the function Q(C) = Ecf(x), where f (x) = ())',x = 0, 1, 2, . zero elsewhere. If C1 = {x : x = 0, 1, 2, 3} and C2 = {x : x = 0, 1, 2, ...}, find Q (C1) and Q(C2). %3D Hint: Recall that Sn = a+ ar + + ar"-1 = a (1- r")/(1 – r) and, hence, it follows that lim,00 Sn = a/ (1 - r) provided that Ir| < 1. !! ... 10
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