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Let (an) be a sequence of real numbers. Using the definition of the limit of a sequence, prove the following results. 5n2 – 7n sin n (a) lim n+0 n2 + 3n +4 (b) If lim a, = L> 0. then there exists an integer N such that 4 an > EL, for all n > N. (c) If lim an = L and lim b, = M then lim a,b, = LM. %3D

Let (an) be a sequence of real numbers. Using the definition of the limit of a sequence, prove the following results. 5n2 – 7n sin n (a) lim n+0 n2 + 3n +4 (b) If lim a, = L> 0. then there exists an integer N such that 4 an > EL, for all n > N. (c) If lim an = L and lim b, = M then lim a,b, = LM. %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1 Let (an) be a sequence of real numbers. Using the definition of the limit of a sequence, prove the following results. (a) lim n+0 n2 + 3n +4 5n2 – 7n sin n = 5. (b) If lim a,, = L> 0. then there exists an integer N such that %3D 4. an >L, for all n N. (c) If lim an = L and lim b, = M then lim anb, = LM. %3D
Transcribed Image Text:1 Let (an) be a sequence of real numbers. Using the definition of the limit of a sequence, prove the following results. (a) lim n+0 n2 + 3n +4 5n2 – 7n sin n = 5. (b) If lim a,, = L> 0. then there exists an integer N such that %3D 4. an >L, for all n N. (c) If lim an = L and lim b, = M then lim anb, = LM. %3D
If a question says to 'use the definition' to prove some result, your answer must rely solely on the definition to prove the result, and not on other results from the course. If the question does not say this then you may use any result from the course in your answer.
Transcribed Image Text:If a question says to 'use the definition' to prove some result, your answer must rely solely on the definition to prove the result, and not on other results from the course. If the question does not say this then you may use any result from the course in your answer.
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