Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
Determine the convergence or divergence of the sequence. If it converges, find the limit. Be sure to justify your reasoning.
![### Mathematical Sequences
#### (a) Sequence Formula
The sequence is defined by the formula:
\[ a_n = \frac{3 + 5n^2}{1 + n} \]
- **Description**: This is a rational sequence where each term \( a_n \) is determined by dividing a quadratic expression \( 3 + 5n^2 \) by a linear expression \( 1 + n \).
#### (b) Sequence Formula
The sequence is given by:
\[ a_n = 2 + (0.86)^n \]
- **Description**: This sequence is composed of a constant term \( 2 \) plus an exponential decay term \( (0.86)^n \). As \( n \) increases, \( (0.86)^n \) approaches zero, and \( a_n \) approaches the constant value \( 2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7d679a1-84c3-4bb8-9ae6-a66cd12a1e51%2F34c98cb1-685b-4be0-9282-55814239e7b4%2Fl9zkx2_processed.png&w=3840&q=75)
Transcribed Image Text:### Mathematical Sequences
#### (a) Sequence Formula
The sequence is defined by the formula:
\[ a_n = \frac{3 + 5n^2}{1 + n} \]
- **Description**: This is a rational sequence where each term \( a_n \) is determined by dividing a quadratic expression \( 3 + 5n^2 \) by a linear expression \( 1 + n \).
#### (b) Sequence Formula
The sequence is given by:
\[ a_n = 2 + (0.86)^n \]
- **Description**: This sequence is composed of a constant term \( 2 \) plus an exponential decay term \( (0.86)^n \). As \( n \) increases, \( (0.86)^n \) approaches zero, and \( a_n \) approaches the constant value \( 2 \).
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