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Please comfirm if the following for D, E and F converges to a specific value or diverges

Please comfirm if the following for D, E and F converges to a specific value or diverges

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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Please comfirm if the following for D, E and F converges to a specific value or diverges.

(a) TRUE FALSE (b) TRUE FALSE (c) TRUE FALSE (d) TRUE FALSE (e) TRUE FALSE (f) TRUE FALSE TRUE FALSE (h) TRUE FALSE If lim an = 0, then series Σn-o an necessarily converges. 72-00 If series E-1000 an converges, then series E-o an converges. 100 -n= If series - an converges, then series Ex=0(50an) converges. 00 If series an converges, then series Σ-0 (an +3 22=0 11) converges. 100, If lim an = 0 and series o bn converges, and if each an, bn > 0, n→∞o bn then series to an converges also. If f(x) dx converges and 0 ≤ f(x) ≤ g(x) for all x ≥ 1, then g(x) dx converges also. If f f (x) dx converges, then ff(x) dx converges also. There is no value of p such that fx dx converges.
Transcribed Image Text:(a) TRUE FALSE (b) TRUE FALSE (c) TRUE FALSE (d) TRUE FALSE (e) TRUE FALSE (f) TRUE FALSE TRUE FALSE (h) TRUE FALSE If lim an = 0, then series Σn-o an necessarily converges. 72-00 If series E-1000 an converges, then series E-o an converges. 100 -n= If series - an converges, then series Ex=0(50an) converges. 00 If series an converges, then series Σ-0 (an +3 22=0 11) converges. 100, If lim an = 0 and series o bn converges, and if each an, bn > 0, n→∞o bn then series to an converges also. If f(x) dx converges and 0 ≤ f(x) ≤ g(x) for all x ≥ 1, then g(x) dx converges also. If f f (x) dx converges, then ff(x) dx converges also. There is no value of p such that fx dx converges.
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