MATH117 Lecture Notes - Lecture 11: Sine Wave, Without Limits, Indeterminate Form
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19 Oct 2017
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A sequence is simply an in nitely long list of numbers, which we usually label as a1, a2, a3, a4, . More precisely, it is a function whose domain is n (the set of natural numbers 1, 2, 3, etc. ), or possibly n plus the number 0. To denote the entire sequence, we write {an} n=1, or just {an}. A sequence may have a formula (for example, ( 1)n (n + 1) . ), or it might not (for example, the sequence {an}, where an is the is the sequence. 3n n=0 population of the world on january 1st of year n). Most of calculus deals with continuous functions of real variables, but we do encounter sequences quite frequently, and they arise quite naturally in applications. Examples: consider a taut string of length l: If the string is plucked, it will vibrate, as a sine wave.
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