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lim Sin(n)

lim Sin(n)

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.5: Inverse Functions
Problem 1SC: Determine whether fx=x is one-to-one.
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Below is the transcription of the mathematical content seen in the image. This will be presented as part of an educational website focusing on calculus concepts: --- ### Calculus: Evaluating Limits #### Problem: Evaluate the limit of the given function as \( n \) approaches infinity: \[ \lim_{n \to \infty} \frac{\sin(n)}{3n} \] --- This limit evaluates the behavior of the function \(\frac{\sin(n)}{3n}\) as the variable \( n \) grows without bound (approaches infinity). A proper understanding of the sine function, which oscillates between -1 and 1, will aid in analyzing how the fraction behaves when the denominator grows infinitely large. --- Feel free to include any additional explanations, graph visualizations, or step-by-step reasoning of the evaluation process to provide a thorough understanding to the reader.
Transcribed Image Text:Below is the transcription of the mathematical content seen in the image. This will be presented as part of an educational website focusing on calculus concepts: --- ### Calculus: Evaluating Limits #### Problem: Evaluate the limit of the given function as \( n \) approaches infinity: \[ \lim_{n \to \infty} \frac{\sin(n)}{3n} \] --- This limit evaluates the behavior of the function \(\frac{\sin(n)}{3n}\) as the variable \( n \) grows without bound (approaches infinity). A proper understanding of the sine function, which oscillates between -1 and 1, will aid in analyzing how the fraction behaves when the denominator grows infinitely large. --- Feel free to include any additional explanations, graph visualizations, or step-by-step reasoning of the evaluation process to provide a thorough understanding to the reader.
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