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3 + 5n2 (а) ат 1+п (b) аn = 2+ (0.86)"

3 + 5n2 (а) ат 1+п (b) аn = 2+ (0.86)"

Calculus: Early Transcendentals
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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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 \( 2 \).
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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